Structure Of Atom Long Questions and Answers
Structure of Atom Questions: 1. Which one of the following is associated with Ans. A = A Broglie wave of longer wavelength—a proton or an I electron moving with the same velocity?
Answer: \(\lambda=\frac{h}{m v}\)
∴ \(\frac{\lambda_p}{\lambda_e}=\frac{m_e}{m_p} \text { Since } m_p>m_{e^{\prime}}\)
∴ \(\lambda_e>\lambda_p\)
Question 2. Mention the difference in angular momentum of the electron belonging to 3p and 4p -subshell.
Answer: In the case of p -p-orbitals, the value of the azimuthal quantum number Is 1. Hut the magnitude of angular momentum of an electron present in any subshell depends on the value of l. It is Independent ofthe value of the principal quantum number n. Orbital angular momentum \(=\sqrt{l(l+1)} \times \frac{h}{2 \pi}\)
Thus, there is no difference in angular momentum of the electrons belonging to 3p and 4p -subshells.
Question 3. Are the differences in energy between successive energy levels of a hydrogen-like atom the same? Explain.
Answer: No, the differences are not the same. The energy of an electron revolving in ‘ n ‘th orbit, En \(=-\frac{2 \pi^2 m z^2 e^4}{n^2 h^2}\)
Hence, the difference in energy between first (n = 1) and second (n = 2) shell, \(E_1-E_2=-\frac{2 \pi^2 m z^2 e^4}{h^2}\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=-\frac{2 \pi^2 m z^2 e^4}{h^2} \times \frac{3}{4}\)
Similarly \(\begin{aligned}
E_2-E_3 & =-\frac{2 \pi^2 m z^2 e^4}{h^2}\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \\
& =-\frac{2 \pi^2 m z^2 e^4}{h^2} \times \frac{5}{36}
\end{aligned}\)
Obviously, E1- E2±E2- E3
Question 4. Energy by associated the expression, with the \(E_n=-\frac{13.6}{n^2} \mathrm{eV}\) orbite V of. Show-atom \(E_{(n+I)}-E_n=\frac{13.6 \times 2}{n^3} \mathrm{eV},\)
Answer: \(E_{(n+1)}-E_n=\left[-\frac{13.6}{(n+1)^2}-\left(-\frac{13.6}{n^2}\right)\right]\)
If the value of n is very large, then (2n + 1)= 2n and
\((n+1) \approx n \quad\)∴ \(E_{(n+1)}-E_n=\frac{13.6 \times 2 n}{n^2 \times n^2}=\frac{13.6 \times 2}{n^3} \mathrm{eV}\)
Structure of Atom Questions
Question 5. de Broglie wavelength of the wave associated with a moving electron and a proton are equal. Show the velocity of the electron is greater than that of the proton.
Answer: According to de-Broglie’s theory applicable to microscopic particles like electron-\(\lambda=\frac{h}{m v}\)[m =maSsofthe moving particle, v = velocity ofthe moving particle].
Now if the mass and velocity of the electron are me and ve and the mass and velocity of the proton are mp and vp respectively then according to the question
\(\frac{h}{m_e v_e}=\lambda=\frac{h}{m_p v_p}\)∴ \(m_e v_e=m_p v_p \quad \text { or, } \frac{v_e}{v_p}=\frac{m_p}{m_e}\)
But, mp > me so, ve > vp (proved)
Question 6. Calculate the accelerating potential that must be applied on a proton beam to give it an effective wavelength of 0.005 nm.
Answer: \(\lambda=\frac{h}{m v}=\frac{6.626 \times 10^{-34}}{1.67 \times 10^{-27} \times v}\)
∴ v = 7.94 x 104m.s-1
If the accelerating potential is V volts, then energy acquired by the proton =eV. This becomes the kinetic energy ofthe proton.
Hence \(e V=\frac{1}{2} m v^2\)
\(e V=\frac{1}{2} m v^2\)∴ v=32.8v
Question 7. The second line of the Lyman series of H-atom coincides with the sixth line of the Paschen series of an ionic species ‘X. Identify ‘X. (Suppose the value of the Rydberg constant, R is the same in both cases)
Answer: For the second line of the Lyman series of H-atom,
For the sixth line of the Paschen series of the species ‘X with atomic number Z, v \(=R Z^2\left(\frac{1}{3^2}-\frac{1}{9^2}\right)\)
Since the Second Line Of Lyman Seriea Coincides With The Sixth Line Of the Paschen Series Of The Species X We Can equate
\(R\left(\frac{1}{1^2}-\frac{1}{3^2}\right)=R Z^2\left(\frac{1}{3^2}-\frac{1}{9^2}\right)\) \(\frac{8}{9}=Z^2 \times \frac{8}{81} \quad \text { or, } Z^2=9\)Z = 3
∴ The Ionic Spec ies Would Be Li2+
Question 8. An element of atomic weight Z consists of two isotopes of mass number (Z-l) and (Z + 2). Calculate the % of the higher isotope.
Answer: Let the % of the higher isotope [mass number (Z + 2) ] be x.
Hence other isotope [mass number (Z- 1) ] will be (100- x)
Average atomic weight (Z) \(=\frac{x(Z+2)+(100-x)(Z-1)}{100}\)
100Z = Zx + 2x+ 100Z- 100- Zx + x
Or, 3x = 100
or, x= 33.3%
Structure of Atom Questions
Question 9. Show that the sum of energies for the transition from n = 3 to n = 2 and from n = 2 to n = 1 is equals to the energy of transition from n = 3 to n = 1 in the case of an H-atom. Are wavelength and frequencies of the emitted spectrum also additive to their energies?
Answer: \(\begin{aligned}
& \Delta E_{3 \rightarrow 2}=R_H\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \\
& \Delta E_{2 \rightarrow 1}=R_H\left(\frac{1}{1^2}-\frac{1}{2^2}\right) \\
& \Delta E_{3 \rightarrow 1}=R_H\left(\frac{1}{1^2}-\frac{1}{3^2}\right)
\end{aligned}\)
From equation (1), (2) and (3) we have,
\(\Delta E_{3 \rightarrow 2}+\Delta E_{2 \rightarrow 1}=R_H\left(\frac{1}{1^2}-\frac{1}{3^2}\right)=\Delta E_{3 \rightarrow 1}\) \(\text { Thus, } \Delta E_{3 \rightarrow 1}=\Delta E_{3 \rightarrow 2}+\Delta E_{2 \rightarrow 1}\)Since, E – hv hence frequencies are also additive but \(E=\frac{h c}{\lambda}\) and thus wavelengths are not additive
Question 10. In the case of a 15X-atom, five valence electrons are. If the spin quantum number of B and R is +1 then find the group(s) of electrons with three of the quantum numbers the same.
Answer: The spin quantum number of ‘R’ is given as \(+\frac{1}{2}\) and hence that of ‘P’ and ‘Q’ will also be \(+\frac{1}{2}\).
Electrons P, Q, and R are in 3p -orbital, so their n and l values i.e., principal and azimuthal quantum numbers will also be the same.
Therefore, P, Q, and R form a group having three quantum numbers the same. Both A and B belong to 3s having the value of n = 3, l = 0 and m = 0. Hence they also have values of three quantum numbers the same.
Question 11. The Schrodinger wave equation for the 2s electron of a hydrogen atom is, \(\psi_{2 s}=\frac{1}{4 \sqrt{2 \pi}}\left[\frac{1}{a_0}\right]^{3 / 2} \times\left[2-\frac{r}{a_0}\right] \times e^{-r / 2 a_0}\) Node is defined as the point where the probability of finding an electron is zero.
Answer:
∴ \(\text { If } r=r_0, \psi_{2 s}^2=0\)
∴ \(\frac{1}{32 \pi}\left(\frac{1}{a_0}\right)^2\left(2-\frac{r_0}{a_0}\right)^2 e^{-r_0 / 2 a_0}=0\)
The only factor that can be zero in the above expression is \(\left(2-\frac{r_0}{a_0}\right)\)
∴ \(2-\frac{r_0}{a_0}=0 ; \quad \text { or, } r_0=2 a_0 \text {. }\)
Question 12. If the uncertainty in the position of a moving electron is equal to its DC Broglie wavelength, prove that Its velocity is completely uncertain.
Answer: Uncertainty in the position of the electron, Ax = λ.
\(\lambda=\frac{h}{p}\) [From de Broglie equation]
∴ \(p=\frac{h}{\lambda}=\frac{h}{\Delta x} \quad \text { or, } \Delta x=\frac{h}{p}\)
According to Heisenberg’s uncertainty principle
∴ \(\Delta x \cdot \Delta p \frac{h}{4 \pi} \quad \text { or, } \frac{h}{p} \cdot \Delta p\frac{h}{4 \pi} \quad \text { or, } \quad \frac{\Delta p}{p}\frac{1}{4 \pi}\)
or, \(\frac{m \Delta v}{m v} \frac{1}{4 \pi} \quad \text { or, } \quad \Delta v \frac{v}{4 \pi}\)
The uncertainty in velocity is so large that its velocity Is uncertain.
Structure of Atom Questions
Question 13. The electron revolving In the n-th orbit of Be3+ ion has the same speed as that of the electron in the ground state of the hydrogen atom. Find the value of n.
Answer: The velocity of an electron in the n-th orbit of hydrogen-like species is given by, \(v_n=\frac{Z}{n} \times v_1\)
[where v1 = velocity of the electron in the 1st orbit of H-atom i.e., the velocity of the electron in the ground state of H-atom and Z = Atomic number of hydrogen-like species]
Now for \(\mathrm{Be}^{3+} \text {-ion } Z=4 \text {, so } v_n=\frac{4}{n} \times v_1\)
But it is given that, v n = v1
∴ \(v_1=\frac{4}{n} v_1 \quad \text { or } n=4\)
Question 14. When Be is bombarded with a -particles, a new element viz carbon Is formed whereas, when gold is bombarded with a -particles, no new elements are formed. Explain.
Answer: There are 79 protons in the nucleus of a gold (7gAu) atom, while o’ -particles are helium nuclei with 2 unit positive charges.
The approaching a -particles are repelled strongly due to high positive charges of Au nuclei and thus suffer deflection.
On the other hand, there are only 4 protons in the nucleus of the beryllium (4Be) atom are very weak compared to those between the gold nuclei and o – particles, due to the low positive charge of the Be nucleus. Thus, the fast-moving a -particles collide with Be nuclei and cause splitting \({ }_4^9 \mathrm{Be}+{ }_2^4 \mathrm{He} \longrightarrow{ }_6^{12} \mathrm{C}+{ }_0^1 n\)
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Question 15. Why are atomic spectra not continuous?
Answer: Each electron in an atom is associated with a definite energy corresponding to different energy levels.
These electrons absorb energy from various external sources (like heat, light, etc.) and are promoted to higher energy-levels. These excited electrons radiate different amounts of energy and return to the ground state.
Structure of Atom Questions
Since the difference between any two energy levels is fixed, the atomic spectra obtained are discontinuous line spectra having fixed wavelengths.
The spectrum so obtained consists of a few bright lines but does not contain all the possible spectral lines corresponding to a range of given wavelengths. Thus, atomic spectra are not continuous.
Question 16. With the help of Bohr’s theory, how will you determine the kinetic energy of hydrogen or hydrogen-like atoms?
Answer: Let the no. of positive charges in the nucleus of a given atom or ion be Z.e (Z = atomic no., e = charge of a proton).
According to Bohr’s theory, the electron present in that atom or ion revolves around the nucleus only in stationary orbits.
Let the radius ofthe stationary orbit be ‘r’ For the stability of the atom, the coulombic force must be equal to the centrifugal force of the electron moving with a velocity \(\frac{Z e^2}{r^2}=\frac{m v^2}{r} \text { or } \frac{1}{2} m v^2=\frac{Z e^2}{2 r}\)
Question 17. What is the precessional motion of the orbit?
Answer: According to Sommerfeld’s relativistic correction of the atomic model, an electron revolves in an elliptical orbit around the nucleus, which is located at the focus of the ellipse. This results in a continual change in the mass and velocity of the electron. The mass of the moving electron increases with its velocity.
The velocity of this electron is maximum when closest to the focus of the ellipse (perihelion) and minimum when farthest from the focus (aphelion). Because of its increased mass at the perihelion, the electron experiences a stronger force of attraction from the nucleus.
This compels the electron to deviate from its original orbit to a new and identical orbit, which lies in the same plane. The perihelion moves each time the electron completes a revolution.
Thus the entire electron orbit moves about an axis passing through the nucleus. This phenomenon is known as Sommerfeld’s precession or precessional motion of the orbit.
Structure of Atom Questions
Question 18. Name the noble gas and give its atomic number if the number of d -d-electrons present in this atom is equal
to the difference in the no. of electrons present in the p and s- s-subshells
Answer: The noble gas is krypton (Kr). Its atomic number = 36
Electronic configuration: ls22s22p63s23p63d104s24p6
- Number of s -electrons = 2 + 2 + 2 + 2 = 8
- Number of p -electrons = 6 + 6 + 6 = 18
- Number of d -electrons = 10
∴ Number of p -electrons number of s -electrons =18-8 = 10= number of d -electrons
Question 19. There is a wavelength limit beyond which the spectrum of any given series of the H-atom becomes Ze2 continuous. Why?
Answer: The energy difference between the first and second orbits is maximum. With the increase in the value of the principal quantum number (n), the energy difference between two successive orbits decreases. Consequently, after a particular value of n, the energy levels become very closely spaced and as a result, they seem to be continuous.
Structure Of Atom Multiple Choice Questions
Question 1. The ionization potential of a hydrogen atom is 13.6 eV. A hydrogen atom in the ground state is excited by monochromatic light of energy 12.1 eV. The spectral lines emitted by hydrogen according to Bohr’s theory will be.
- One
- Two
- Three
- Four
Answer: 3. Three
Question 2. The number of waves made by a Bohr electron in an orbit of maximum magnetic quantum number 3 is-
- 4
- 3
- 2
- 1
Answer: 1. 4
Structure of Atom Questions
Question 3. In which of the following cases would the probability of finding an electron residing in a d -d-orbital be zero
- xz and yz -planes
- xy and yz -planes
- z -direction, yz and xz -plane
- xy and xz -planes
Answer: 1. xz and yz -planes
Question 4. An electron beam with a de Broglie wavelength of P A is accelerated till its wavelength is halved. By what factor will kinetic energy change
- 2
- 1/4
- 4
- none
Answer: 3. 1/4
Question 5. If the Aufbau rule is not followed then the percent change in total (n + l) value for unpaired electrons in 25Mn is-
- 60
- 50
- 40
- 30
Answer: 3. 40
Structure of Atom Questions
Question 6. If the shortest wavelength of the IT -atom in the Lyman series is X, then the longest wavelength in the Paschen series of He+ is
- \(\frac{36 X}{5}\)
- \(\frac{36 X}{7}\)
- \(\frac{7 X}{36}\)
- \(\frac{6 X}{5}\)
Answer: 2. \(\frac{36 X}{7}\)
Question 7. The atomic numbers of elements X, Y, and Z are 19, 21, and 25 respectively. The number of electrons present in the ‘M’ shells of these elements follows the order —
- Z<Y<x
- X<y<Z
- Z>X>Y
- Y>Z>X
Answer: 1. Z<Y<x
Question 8. Hydrogen atoms are excited in the n = 4 state. In the spectrum of the emitted radiation, the number of lines in the ultraviolet and visible regions are respectively—
- 2:3
- 3:1
- 1:3
- 3:2
Answer: 4. 3:2
Question 9. Which orbital has only a positive value of wave function at all distances from the nucleus—
- 3d
- 2p
- 2s
- 1s
Answer: 4. 1s
Structure of Atom Questions
Question 10. The number of photons of light having wave number ‘a’ in the 32 energy source is
- \(\frac{h c}{3 a}\)
- 3hca
- \(\frac{3}{h c a}\)
- \(\frac{3}{h c a}\)
Answer: 3. \(\frac{3}{h c a}\)
Question 11. The wavelength of the de Broglie wave of the electron in the sixth orbit of-atom is—( rQ = Bohr’s radius
- πr0
- 12πr0
- 6πr0
- 24πr0
Answer: 2. 12πr0
Question 12. In an orbit, the velocity of an electron in the excited state of Hatom is 1.093 X 108 cm-s-1. The circumference of this orbit is —
- 13.3A
- 6.65A
- 3.33A
- 26.65A
Answer: 1. 13.3A
Question 13. Which have the largest number of unpaired electrons in p -p-orbitals in their ground state electronic configurations—
- Te, I, Xe
- F, Cl, Br
- Ne, Ar, K
- N, P, As
Answer: 4. N, P, As
Structure of Atom Questions
Question 14. Which orbitals have two nodal planes passing through the nucleus —
- de
- p
- s
- None
Answer: 1. de
Question 15. Compared to the mass of the lightest nuclei, the mass of an electron is only-
- 1/80
- 1/800
- 1/1800
- 1/2800
Answer: 3. 1/1800
Question 16. Among the following sets of quantum numbers, which one Is Incorrect for 4d -electrons-
- \(4,3,2,+\frac{1}{2}\)
- \(4,3,2,+\frac{1}{2}\)
- \(4,2,-2, \frac{1}{2}\)
- \(4,2,1, \frac{-1}{2}\)
Answer: 2. \(4,3,2,+\frac{1}{2}\)
Question 17. Which d -orbitals have a different shape from the rest of all d orbitals—
- \(d_{x^2-y}\)
- dx
- dz2
- dyz
Answer: 3. dz2
Structure of Atom Questions
Question 18. Which element possesses non-spherical shells
- he
- B
- Be
- Li
Answer: 2. B
Question 19. Which have the same number of s -electrons as the d electrons In Fe2+
- li
- Na
- Na
- Fe
Answer: 4. Fe
Question 20. An anion X3 has 36 electrons and 45 neutrons. What is the mass number ofthe element X-
- 81
- 84
- 78
- 88
Answer: 3. 78
Question 21. Consider the set of quantum numbers \(3,2,-2,+\frac{1}{2}\), if the given subshell is filled. The next electron will enter orbital with n and l value—
- n=3, l=3
- n=4,l=1
- n=1,l=1
- n=2,l-1
Answer: 2. n=4,l=1
Structure of Atom Questions
Question 22. Given that an orbital is symmetric about the nucleus, then the value of azimuthal quantum number and magnetic quantum number are respectively
- -1+1
- +1+1
- 0,0
- 1,0
Answer: 3. 0,0
Question 23. A certain F.M. station broadcasts at a wavelength equal to 3.5 m. How many photons per second correspond to the transmission of one kilowatt–
- 2.24×1027
- 1.76×1028
- 2.26×1028
- 1.43×1026
Answer: 2. 1.76×1028
Question 24. A Bohr orbit in H-atom has a radius of 8.464 A. How many transitions may occur from this orbit to the ground state-
- 10
- 3
- 6
- 15
Answer: 3. 6
Question 25. The angular momentum of the electron in the 4/-orbital of a one-electron species according to wave mechanics is —
- \(\sqrt{3} \frac{h}{\pi}\)
- \(2 \frac{h}{\pi}\)
- \(\sqrt{\frac{3}{2}} \frac{h}{\pi}\)
- \(\sqrt{\frac{1}{2}} \frac{h}{\pi}\)
Answer: 1. \(\sqrt{3} \frac{h}{\pi}\)
Structure of Atom Questions
Question 26. Consider the Structure of the ground Atom Mato of cnCr atom (z= 24).-The1 number of electrons with the azimuthal quantum numbers, =1 and 2 nrc respectively
- 12 and 4
- 12 and 5
- 16 and 4
- 16 and 5
Answer: 2. 12 and 5
Question 27. The magnetic moment of Mx+ (atomic number of M = 25 ) is Jl5 BM. The number of unpaired electrons and the value of x respectively are—
- 5,2
- 3,2
- 3,4
- 4,3
Answer: 3. 3,4
Question 28. Radial part of the wave function depends upon quantum numbers
- n and s
- 1 and m
- 1 and s
- n and 1
Answer: 1. n and s
Question 29. Which ofthe following pairs of nuclides are in diapers
- \({ }_6^{13} \mathrm{C} \text { and }{ }_8^{16} \mathrm{O}\)
- \({ }_6^{13} \mathrm{C} \text { and }{ }_8^{16} \mathrm{O}\)
- \({ }_1^3 \mathrm{H} \text { and }{ }_2^4 \mathrm{He}\)
- \({ }_{25}^{55} \mathrm{Mn} \text { and }{ }_{30}^{65} \mathrm{Zn}\)
Answer: 4. \({ }_{25}^{55} \mathrm{Mn} \text { and }{ }_{30}^{65} \mathrm{Zn}\)
Structure of Atom Questions
Question 30. The dissociation energy of H2 is 430.53 kfrmol-1. If hydrogen is dissociated by illumination with radiation of wavelength 253.7 nm, the fraction of the radiant energy that will be converted into kinetic energy is given by
- 100%
- 8.76%
- 2.22%
- 1.22%
Answer: 2. 8.76%
Question 31. The correct order of penetrating power of 3s, 3p, and 3d electrons is
- 3d>3p>3s
- 3s>3p>3d
- 3s>3p>3d
- 3d>3s>3p
Answer: 3. 3s>3p>3d
Question 32. Hund’s rule pertains to the distribution of electrons in
- Principal energy shell
- An orbital
- Degenerate
- None of these
Answer: 3. Degenerate
Question 33. A principal shell having the highest energy subshell to be V can accommodate electrons to a maximum of—
- 18
- 32
- 25
- 50
Answer: 4. 50
Question 34. When an electron of H-atom jumps from a higher to lower energy, then—
- Its potential energy increases
- Its kinetic energy increases
- Its angular momentum remains unchanged
- Its de Broglie wavelength increases
Answer: 4. Its de Broglie wavelength increases
Structure of Atom Questions
Question 35. What will be the number of spectral lines (AO observed if an electron undergoes a transition from n2 excited level to nl excited level in an atom of hydrogen—
- \(N=\frac{\left(n_2-n_1\right)\left(n_2-n_1+1\right)}{2}\)
- \(N=\frac{\left(n_1-n_2\right)\left(n_2-n_1+1\right)}{2}\)
- \(N=\frac{\left(n_2+n_1\right)\left(n_1+n_2+1\right)}{2}\)
- N = 2(nl-n2)(n2 + n1-l)
Answer: 1. \(N=\frac{\left(n_2-n_1\right)\left(n_2-n_1+1\right)}{2}\)
Question 36. The given diagram indicates the energy levels of certain atoms. When the system moves from 2E level to E, a photon of wavelength X is emitted. The wavelength of photon produced during its transition from level to E iS-
- \(\frac{3 \lambda}{3}\)
- \(\frac{4}{3} \lambda\)
- 3 lambada
Answer: 4. 3 lambada
Question 37. Electromagnetic radiation with maximum wavelength Is-
- Ultraviolet
- Radiowaves
- X-way
- infrared
Answer: 2. Radiowaves
Question 38. Brackett series are produced when the electrons from the outer orbits jump to—
- 2nd orbit
- 3rd orbit
- 4th orbit
- 5th orbit
Answer: 3. 4th orbit
Question 39. The following sets that do NOT contain isoelectronic species—
- \(\mathrm{BO}_3^{3-}, \mathrm{CO}_3^{2-}, \mathrm{NO}_3^{-}\)
- \(\mathrm{SO}_3^{2-}, \mathrm{CO}_3^{2-}, \mathrm{NO}_3^{-}\)
- \(\mathrm{CN}^{-}, \mathrm{N}_2, \mathrm{C}_2^{2-}\)
- \(\mathrm{PO}_4^{3-}, \mathrm{SO}_3^{2-}, \mathrm{ClO}_4^{-}\)
Answer: 2. \(\mathrm{SO}_3^{2-}, \mathrm{CO}_3^{2-}, \mathrm{NO}_3^{-}\)
Question 40. The hydrogen-like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon absorbing light, the ion undergoes a transition to a state S2. The state S2 has one radial node and its energy is equal to the ground state energy ofthe hydrogen atom-
The state is
- 1s
- 2s
- 2p
- 3s
Answer: 2. 2s
Structure of Atom Questions
Question 41. The energy of the state S1 in units of the hydrogen atom ground state energy is-
- 0.75
- 1.50
- 2.25
- 4.50
Answer: 3. 2.25
Question 42. In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005% certainty with which the position ofthe electron can be located is{h = 6.6 x 10-34 kg-m2 s_1, mass of electron, mg = 9.1 x 10-31 kg).
- 3.84 x 10-3 m
- 1.52x 10-4 m
- 5.10×10-3m
- 1.92 x 10-3m
Answer: 2. 1.52x 10-4 m
Question 43. The ionization enthalpy of a hydrogen atom is 1.312 x 106J-mol-1. The energy required to excite the electron in the atom from n – 1 to n = 2 is
- 7.56 X 105 J-mol-1
- 9.84 X105 J-mol-1
- 8.51 x 105 J-mol-1
- 6.56 X 105 J-mol-1
Answer: 2. 9.84 X105 J-mol-1
Structure of Atom Questions
Question 44. If we apply potential difference so that an electron is accelerated continuously in a vacuum tube such that a decrease of 10% occurs in its de-Broglie wavelength. In such a case the change observed in the kinetic energy of the election will be approximately—
- A Decrease Of 11%
- An increase of 11.1%
- An Increase Of 10%
- An increase of 23.4%
Answer: 4. An increase of 23.4%
Question 45. The approximate wavelength of matter wave associated with an electron, that is accelerated by applying 100 V of potential difference in a discharge tube, will be-
- 123pm
- 12.3pm
- 1.23 pm
- 0.123pm
Answer: 1. 123pm
Question 46. If two particles are associated with the same kinetic energy, then the de Broglie’s wavelength (A) ofthese particles is—
- Directly proportional to the velocity
- Inversely proportional to the velocity
- Independent of mass and velocity
- Cannot be predicted.
Answer: 1. Directly proportional to the velocity
Structure of Atom Questions
Question 47. The ratio of magnetic moments of Fe (3) and CO (2) is
- \(\sqrt{3}: \sqrt{7}\)
- \(\sqrt{3}: \sqrt{7}\)
- 7:3
- 3:7
Answer: 2. \(\sqrt{3}: \sqrt{7}\)
Question 48. If it were possible for a hydrogen atom to exist with a position as the extra-nuclear particle, then the energy of position in the first excited state would be—
- 13.6v
- 3.4ev
- -3.4ev
- 6.8ev
Answer: 2. 3.4ev
Question 49. Identify the orbitals for which n = 4 and / = 1 —
- 4py
- 4px
- 4dxy
- 4dx2-y2
Answer: 1. 4py
Structure of Atom Questions
Question 50. The orbitals which have the same number of nodes are
- 2s,3p
- 3p,3d
- 2s,2p
- 3s,4d
Answer: 2. 3p,3d
Question 51. In the ground state, an element has 13 electrons in its Afshell. The element is
- Mn
- Cr
- Ni
- Fe
Answer: 1. Mn
Question 52. The angular momentum of an electron may have the values—
- \(0.5 \frac{h}{\pi}\)
- \(\frac{h}{\pi}\)
- \(0.2 \frac{h}{\pi}\)
- \(2.5 \frac{h}{2 \pi}\)
Answer: 1. \(0.5 \frac{h}{\pi}\)
Structure of Atom Questions
Question 53. The line spectrum is noticed during the transition of an electron from a higher excited state to a lower one in the H-atom only when it falls from
- 2s→ls
- 2p→ls
- 3s→2p
- 4p→2p
Answer: 3. 3s→2p
Question 54. Select the pair of atoms having the same no. of electrons in their outermost shell —
- Na, Ca
- Mg, Fe
- As, Bi
- Rb, Sb
Answer: 3. Rb, Sb
Question 55. Which consists of particles of matter—
- a -rays
- 0 -rays
- y -rays
- X-rays
Answer: 1. a -rays
Structure of Atom Questions
Question 56. Which have two radial nodes-
- 2p
- 3s
- 4p
- 3p
Answer: 2. 3s
Question 57. The ratio of λα to λβ for the Balmer series ofhydrogen spectra is given by
- \(\frac{108}{80}\)
- \(\frac{108}{90}\)
- \(\frac{40}{54}\)
- \(\frac{20}{27}\)
Answer: 1. \(\frac{108}{90}\)
Question 58. Indicate the conditions under which the ratio of Broglie wavelengths of a -particle and a proton will be—
- When the ratio of their velocities is 4: 1
- When the ratio of their velocities is 1: 8
- When the ratio of their energies is 128: 1
- When the ratio of their velocities is 1: 16
Answer: 2. When the ratio of their velocities is 1: 8
Structure of Atom Questions
Question 59. Which ofthe following ions is paramagnetic—
- Zn2+
- Cu2+
- He+2
- O2-
Answer: 2. Cu2+
Question 60. The energy of an electron in the first Bohr orbit of the H-atom is -13.6 eV. Then, which of the following statement(s) is/ are correct for He+ —
- The energy of electron in the second Bohr orbit is -13.6 ev
- Kinetic energy of electron in the first orbit is 54.46 ev
- Kinetic energy of electron in second orbit is 13.6 ev
- The speed of an electron in the second orbit is 2.19 x 106m-s-1
Answer: 1. Energy electron in second Bohr orbit is -13.6 ev
Structure of Atom Questions
Question 61. For which of the following species, the expression for the 13 6Z2 eV-atom-1 energy of an electron in nth orbit, En = \(-\frac{13.6 Z^2}{n^2}\) eV. Atom-1. has the validity—
- He2+
- Li2+
- Deuterium
- Li2+
Answer: 2. He2+
Question 62. According to Bohr’s atomic theory, which of the following relations is correct—
- The kinetic energy of electron oc z2/ n2
- The product of the velocity of the electron and the principal quantum number oc z2
- Frequency of revolution of the electron in an orbit zp/n3
- Coulombic force of attraction on electron oc z3/n4
Answer: 1. Kinetic energy of electron oc z2/ n2
Structure of Atom Questions
Question 63. Which is correct in the case of p -p-orbitals—
- They are spherically symmetrical
- They have strong directional character
- They are three-fold degenerate
- Their charge density along the x, y, and z -axes is zero
Answer: 2. They have strong directional character
Question 64. An isotone of \(\mathrm{f}_{32}^{76} \mathrm{Ge}\) is –
- \({ }_{32}^{77} \mathrm{Ge}\)
- \({ }_{33}^{77} \mathrm{As}\)
- \({ }_{34}^{77} \mathrm{Se}\)
- \({ }_{34}^{77} \mathrm{Se}\)
Answer: 2. \({ }_{33}^{77} \mathrm{As}\)
Question 65. Which of the following is correct—
- Only the Lyman series is observed in both emission and absorption spectrum
- The continuum in the line spectrum is noticed after a certain value of n
- the wavelength of the mth line of Balmer Series is \(\frac{1}{\lambda}=R_H Z^2\left[\frac{1}{2^2}-\frac{1}{m^2}\right]\)
- The number of spectral lines given when an electron drops from the 5th to the 2nd shell is six.
Answer: 1. Only the Lyman series is observed in both the emission and absorption spectrum
Structure Of Atom Very Short Answer Type Questions
Question 1. What is the value of the elm of an electron?
Answer: 1.76 x 108Cg-I/
Question 2. How many times a proton is heavier than an electron?
Answer: 1837 times (approx.),
Question 3. Mention one similarity between isobar and isotone-
Answer: Atoms of different elements,
Question 4. What is wave number?
Answer: No. of waves in 1 cm,
Question 5. Arrange in order of the increasing wavelength
Answer: γ-ray
Question 6. What is meant by stationary orbit?
Answer: Orbits in which the energy of revolving electrons remains fixed
Structure of Atom Questions
Question 7. Who proposed the quantum theory of radiation?
Answer: M. Planck
Question 8. What is the value of Planck’s constant in the SI unit?
Answer: 6.626×10-34
Question 9. What is the value of the angular momentum of an electron
occupying the second orbit in an atom?
Answer: \(\frac{h}{\pi}\)
Question 10. Mention the symbol and the mass number of an element
which contains two neutrons in the nucleus.
Answer: \({ }_2^4 \mathrm{He}\)
Question 11. Why is the spectrum of H+ not obtained?
Answer: Because H+ does not contain any electrons,
Question 12. How many proton(s) & electron(s) are in H- ion?
Answer: One proton and two electrons,
Structure of Atom Questions
Question 13. From which principal energy state, the excited electron
comes down to yield spectral lines in the Balmer series?
Answer: L-shell (n = 2),
Question 14. How many neutrons are present in 2oCa2+ ion?
Answer: 20 neutrons,
Question 15. What is the nature of hydrogen spectra?
Answer: Discontinuous spectrum or line spectrum,
Question 16. Mention one ion that obeys Bohr’s theory.
Answer: He+,
Question 17. Write the relationship between wavelength and momentum of a moving microscopic particle. Who proposed this relationship?
Answer: \(\lambda=\frac{h}{m v}\)
Question 18. Indicate the limitation of Broglie’s equation.
Answer: Not applicable to macroscopic particles,
Question 19. Is the uncertainty principle applicable to stationary electrons?
Answer: Not applicable
Structure of Atom Questions
Question 20. Energy associated with which of the following waves is not quantized?
- Electromagnetic wave
- Matter-wave
Answer: Matter waves,
Question 21. What is an orbital according to quantum mechanical
model?
Answer: The region around the nucleus has the maximum probability of finding an electron,
Question 22. How do you specify an electron in an atom?
Answer: By using four quantum numbers (n, l, m and s),
Question 23. What is the maximum number of orbitals in the ‘j’th orbit?
Answer: n2,
Question 24. Which is the lowest energy level containing ‘g1 sub-shell?
Answer: n = 5 (fifth shell),
Question 25. Identify the orbital with n = 4 and 1 = 0.
Answer: 4s,
Question 26. Which ‘d’-orbital does not contain four lobes?
Answer: dz2,
Question 27. Which quantum electron?
Answer: Azimuthal quantum number (/),
Structure of Atom Questions
Question 28. Write the electronic configuration of Mn
Answer: ls22s22p63s23p63d5,
Question 28. What is the total number of nodes in 3d -orbital?
Answer: Total no. of nodes =(n-l) =3- 1 = 2 ,
Question 30. Which subshell has the lowest screening power?
Answer: F
Question 31. Which quantum number is used to distinguish between the electrons present in a single orbital?
Answer: Spin quantum number, S,
Question 32. What are the quantum numbers used to indicate the size and shape of orbitals?
Answer: Principal & azimuthal quantum numbers,
Question 33. State the condition under which electronic energy is considered to be negative.
Answer: When the electron is at an infinite distance from the nucleus ( n = oo )
Structure Of Atom Fill In The Blanks
Question 1. The cgs unit of Planck’s constant is unit is _____________
Answer: erg-s, J.s,
Question 2. The angular momentum of an electron in the nth orbit is _____________ 2+ ion.
Answer: nhl2n,
Question 3. If an a -particle and two (i -particles are emitted from a radioactive element, the element produced becomes an _____________ofthe parent element.
Answer: isotope,
Question 4. With the help of Bohr’s atomic model, the idea of _____________quantum number was first obtained.
Answer: principal,
Structure of Atom Questions
Question 5. Bohr’sunitatomic of Rydberg’smodel ignored constant _____________
Answer: three-dimensional,
Question 6. The unit of Rydergs’s Constant In CGS UNit is _____________
Answer: Cm-1
Question 7. The range of wavelength of visible light is _____________
Answer: 4000-8000A,
Question 8. The ionization potential of hydrogen is _____________
Answer: cm-1
Question 9. Uhlenbeck and Goudsmit introduced the concept of_____________ quantum number.
Answer: 13.54eV,
Question 10. The product of uncertainties in the position and momentum ofan the electron is always equal to or greater than_____________
Answer: Spin,
Question 11. The product of uncertainties in the position and momentum of electron is always equal to or greater than_____________
Answer: h/4n,
Question 12. The number of magnetic quantum numbers required to describe the electrons of-subshell is _____________
Answer: 1. 12.5
Numerical Examples
Question 1. A sample of gaseous oxygen contains only 180 isotopes. How many neutrons are present in 11.2 L of the gas at STP?
Answer: No. of neutrons present in an atom of 180 isotope
=(18-8) = 10
∴ No. of neutrons present in 11.2L ofthe gas
\(=\frac{2 \times 10 \times 6.022 \times 10^{23} \times 11.2}{22.4}=6.022 \times 10^{24}\)Structure of Atom Questions
Question 2. Calculate the energy required for the promotion of electrons from the 1st to 5th Bohr orbit of all the atoms present in 1 mole of H-atoms.
Answer: Electronic energy in the n-th orbit ofH-atom
∴ Total energy required
\(=\left(E_5-E_1\right)=-\frac{1312}{5^2}-\left(-\frac{1312}{1^2}\right)=1259.52 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\)Question 3. Calculate the velocity (cm-s-1) and frequency of revolution of electron present in the 3rd orbit of H-atom.
Answer: Velocity of revolving electron present in the 3rd orbit of H atom
Frequency of revolution ofthe electron
\(=\frac{v}{2 \pi r}=\frac{v}{2 \pi\left(\frac{n^2 h^2}{4 \pi^2 m z e^2}\right)}=\frac{2 \pi m v z e^2}{n^2 h^2}\) \(=\frac{2 \times 3.14 \times\left(9.11 \times 10^{-28}\right) \times\left(7.27 \times 10^7\right) \times 1 \times\left(4.8 \times 10^{-10}\right)^2}{(3)^2 \times\left(6.626 \times 10^{-27}\right)^2}\)= 2.4242×1014
Question 4. Calculate the wavelength and frequency associated with the spectral line having the longest wavelength in the fund series of hydrogen spectra.
Answer: In the case of the Pfund series, the spectral line with the longest wavelength is obtained when the electronic transition occurs from n2 = 6 to nl = 5. Thus
\lambda=7.4 \times 10^{-4} \mathrm{~cm} & \\
v=\frac{c}{\lambda}=\frac{3 \times 10^{10}}{7.4 \times 10^{-4}} & =4.05 \times 10^{13} \mathrm{~s}^{-1} \\
& =4.05 \times 10^{13} \mathrm{~Hz}
\end{aligned}\)
Question 5. Calculate the energy of 1 mol of photons associated with a frequency of 5 x 1010s-1.
Answer: \(\begin{aligned}
E=N_0 h v & =6.022 \times 10^{23}\left(6.626 \times 10^{-34}\right)\left(5 \times 10^{10}\right) \\
& =19.95 \mathrm{~J}
\end{aligned}\)
Structure of Atom Questions
Question 6. The wavelength associated with a moving particle of mass
0.1 mg is 3.3 x 10-29m . Find its velocity.
[h = 6.6 X 10~34 kg-m2-s_1]
Answer: \(\begin{aligned}
& \lambda=\frac{h}{m v} \\
& \text { or, } v=\frac{h}{m \lambda}=\frac{6.6 \times 10^{-34}}{\left(0.1 \times 10^{-6}\right) \times\left(3.3 \times 10^{-29}\right)}=200 \mathrm{~m} \cdot \mathrm{s}^{-1}
\end{aligned}\)
Question 7. Calculate the kinetic energy of a moving electron associated with a wavelength of 4.8 pm.
Answer: \(\begin{aligned}
\nu & =\frac{h}{m \lambda}=\frac{6.626 \times 10^{-34} \mathrm{~kg} \cdot \mathrm{m}^2 \cdot \mathrm{s}^{-1}}{\left(9.11 \times 10^{-31} \mathrm{~kg}\right) \times\left(4.8 \times 10^{-12} \mathrm{~m}\right)} \\
& =1.51 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}
\end{aligned}\)
Kinetic energy
\(\begin{aligned}& =\frac{1}{2} \times\left(9.11 \times 10^{-31} \mathrm{~kg}\right) \times\left(1.51 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\right)^2 \\
& =1.038 \times 10^{-14} \mathrm{~J}
\end{aligned}\)
Question 8. Calculate the frequency and wavelength of the energy emitted when the electron jumps from the 4th orbit to the 1st orbit of the H-atom.
Answer: \(\bar{v}=\frac{1}{\lambda}=1.09678 \times 10^7 \times\left(\frac{1}{1^2}-\frac{1}{4^2}\right)=10.28 \times 10^6 \mathrm{~m}^{-1}\)
Question 9. The wavelength of the first line in the Balmer series of H-atom is 15200 cm-1. Calculate the wavelength of the first line in the same series of Li2+ ions. 10. The ionization potential of sodium is 4.946 x 102kJ-mol-1. Calculate the wavelength of the radiation required to ionize a sodium atom
\(\begin{aligned}& \bar{v}_{\mathrm{H}}=R_H\left(\frac{1}{2^2}-\frac{1}{n^2}\right)=15200 \mathrm{~cm}^{-1} \\
& \bar{v}_{\mathrm{Li} \mathrm{i}^{3+}}=\bar{v}_{\mathrm{H}} \times z^2=15200 \times 3^2=136800 \mathrm{~cm}^{-1}
\end{aligned}\)
Structure of Atom Questions
Question 11. The wavelength range of the visible spectrum extends from violet (400 nm) to red (750 nm). Express these wavelengths in frequencies (Hz) (Inm = 10~9m)
Answer: For violet light, \(v_1=\frac{c}{\lambda_1}=\frac{3 \times 10^8}{400 \times 10^{-9}}=7.5 \times 10^{14} \mathrm{~Hz}\)
For red light, \(v_2=\frac{c}{\lambda_2}=\frac{3 \times 10^8}{750 \times 10^{-9}}=4.0 \times 10^{14} \mathrm{~Hz}\)
Thus the frequency range of visible light extends from 11.0 X 1014HZ to 7.5 x 1014Hz.