Modern Physics
Each of the following questions comprises two statements. The assertion is expressed by Statement 1 and the reason is expressed by Statement 2.
Each question has four options (1), (2), (3), and (4) as given below, out of which only ONE is correct.
- Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
- Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
- Statement 1 is true and Statement 2 is false.
- Statement 1 is false and Statement 2 is true.
- Both Statement 1 and Statement 2 are false.
Some questions are preceded, by a supporting paragraph in addition to the statements.
Photoelectric Effect Matter Waves
Question 1. Statement 1 A photon has no rest mass, yet it carries a definite momentum.
Statement 2 The momentum of a photon is due to its energy and henceit has an equivalent mass.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
A particle that travels at the speed of light (a photon) has a zero rest mass but has an energy of E =hf and momentum of \(p=\frac{h}{\lambda}=\frac{E}{c}\)
Question 2. Statement 1 The energy (E) and momentum (p) of a photon are related by \(p=\frac{E}{c}\)
Statement 2 A photon behaves like a particle.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The energy of a photon of frequency f is E = hf and its momentum is \(p=\frac{h}{\lambda}=\frac{E}{c}\).
A photon has a particle nature to describe the photoelectric effect.
Question 3. Statement 1 When light of a certain wavelength falls on a metal surface, it ejects electrons.
Statement 2 Light has a wave nature.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
When a light of a wavelength less than the threshold wavelength strikes a photosensitive surface, photoelectrons are ejected. This is explained by the photon (particle) theory. But light has a dual (both particle and wave) nature.
Question 4. Statement 1 On increasing the frequency of light, a larger number of photoelectrons are emitted.
Statement 2 The maximum KE of electrons emitted is directly proportional to the intensity of the incident light.
Answer: 5. Both Statement 1 and Statement 2 are false.
The number of photoelectrons ejected is directly proportional to the intensity of the incident light and not to the frequency of the incident light. The maximum KE of the emitted photoelectrons depends on the frequency and not on the intensity of the incident radiation.
Read And Learn Also NEET Physics Multiple Choice Question and Answers
Question 5. Statement 1 There is a physical significance of matter waves.
Statement 2 Both interference and diffraction are displayed by matter waves.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Particles exhibit a wave nature as well. They can be diffracted (as in the Davisson-Germer experiment) and the phenomenon of matter-wave interference lies at the heart of quantum physics.
Question 6. Statement 1 The relative velocity of two photons travelling in opposite directions is the velocity of light.
Statement 2 The rest mass of a photon is zero.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
According to the theory of relativity, speed cannot exceed that of light in a vacuum (c = 3 x102 m s-1). Photons travel at the speed of light, and their relative velocity when moving apart will be c. The rest mass of a particle traveling at the speed of light is zero. This follows from the equation
∴ \(m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}\)
physics multiple choice questions
Question 7. Statement 1 An electron microscope is based on the de Broglie hypothesis.
Statement 2 A beam of electrons behaves as a wave that is converged by electric and magnetic lenses.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
In an electron microscope, a beam of accelerated electrons is used. Its de Broglie wavelength,
∴ \(\lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m e V}}\),
can be around 105 times shorter than that of the visible light (photons). Electric and magnetic fields are used to converge or diverge the electron beam. These fields are analogous to the glass lenses of an optical microscope.
Question 8. Statement 1 The de Broglie equation has significance for microscopic or submicroscopic particles.
Statement 2 The de Broglie wavelength is inversely proportional to the mass of the objectifies velocity is constant.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The de Broglie wavelength \(\left(\lambda=\frac{h}{m v}\right)\) has an appreciable value for a particle with a small mass like that of a subatomic particle.
Question 9. Statement 1 The second postulate of the special theory of relativity refers to the velocity of light in a vacuum.
Statement 2 A Cerenkov radiation results when particles move through a transparent medium at a speed greater than that of light in that medium. It does not violate the second postulate of the special theory.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Cerenkov radiation occurs when some particles move through a transparent medium at a speed more than the speed of light in the medium.
Still, the particle’s speed is less than the speed of light in a vacuum. So, the second postulate of special relativity is not violated.
Question 10. Statement 1 Stopping potential depends upon the frequency of the incident light but is independent of the intensity of light.
Statement 2 The maximum kinetic energy of photoelectrons is proportional to the stopping potential.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
According to Einstein’s equation of photoelectric effect, \(h v=\phi_0+\mathrm{KE}_{\max } \text {, where } \mathrm{KE}_{\max }=e V_{\mathrm{st}}\).
Thus, the stopping potential Vst depends upon v, the frequency of the incident light. Further, KEmax is proportional to Vst.
Question 11. Statement 1 The photoelectric effect demonstrates the wave nature of light.
Statement 2 The number of photoelectrons is proportional to the frequency of light.
Answer: 5. Both Statement 1 and Statement 2 are false.
The photoelectric effect corresponds to the particle nature (photon) of light, not its wave nature.
The photoelectric current is proportional to the intensity of light and not to the frequency of light.
“quiz questions in physics with answers “
Question 12. Statement 1 The maximum kinetic energy of the emitted photoelectrons changes only, with a change in the frequency of the incident radiation.
Statement 2 The kinetic energy of the emitted photoelectrons depends on the intensity of the incident light.
Answer: 3. Statement 1 is true and Statement 2 is false.
From the equation, hv = Φ0 + KEmax, the work function (Φ0) is constant for a metal.
KEmax changes only with a change in the frequency (v) of light.
The intensity of the incident light can change only the photoelectric current and not the maximum kinetic energy of the emitted electrons.
Question 13. Statement 1 The photoelectrons produced by a monochromatic light beam incident on a metal surface have a spread of their kinetic energies.
Statement 2 The work function of the metal varies as a function of the depth from the surface.
Answer: 3. Statement 1 is true and Statement 2 is false.
The spread of kinetic energy of the emitted photoelectrons is due to the collisions of free electrons before emissions. The work function (Φ0) is constant for a metal.
Bohr Model Hydrogen Spectrum
Question 1. Statement 1 The total energy of an electron in a hydrogen atom is negative.
Statement 2 It is bound to the nucleus.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The electron in the H atom is bound to the nucleus by an electrostatic force and hence has a negative energy.
Question 2. Statement 1 In a metal, all the free electrons have the same energy.
Statement 2 Electrons do not obey Pauli’s exclusion principle.
Answer: 3. Statement 1 is true and Statement 2 is false.
Free electrons in a metal occupy a single energy band and so have the same energy. Electrons in a metal always follow the Pauli exclusion principle.
Question 3. Statement 1 Lasers are used to measure the distances of distant objects such as the moon.
Statement 2 They are highly coherent sources of light.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Lasers are focused, intense, narrow, and highly energetic coherent sources of light, which can travel through large distances before divergence. Hence, these are used to measure large distances.
Question 4. Statement 1 Bohr postulated that the orbital electrons in the stationary orbits around the nucleus do not radiate.
Statement 2 According to classical physics, all moving electrons radiate.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
The Bohr postulate refers to ‘stationary orbits’ for the electrons which are non-radiating.
According to the classical theory, an accelerated charge always radiates. But this is not true in the Bohr theory, as circular motion is an accelerated motion.
Question 5. Statement 1 Crystalline solids can cause X-rays to diffract.
Statement 2 Interatomic spacings in crystalline solids are of the order of 0.1 nm.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The lattice spacing crystals (≈ 0.1 nm) are of the order of wavelengths of X-rays and hence act as a three-dimensional grating to produce diffraction.
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Question 6. Statement 1 A laser beam of 0.2 W can drill holes through a metal sheet, whereas a 1000-W torchlight cannot.
Statement 2 The frequency of a laser beam is much higher than that of a torchlight.
Answer: 3. Statement 1 is true and Statement 2 is false.
A laser beam is a highly intense, coherent, monochromatic, and parallel beam of light, which can be converted to a very small spot by a convex lens to drill a hole. Light from a 1000-W source cannot drill a hole, because such light has less intensity and the beam is not a parallel one.
Question 7. Statement 1 It is essential that all the lines available in the emission spectrum will also be available in the absorption spectrum.
Statement 2 The spectrum of a hydrogen atom is only an absorption spectrum.
Answer: 5. Both Statement 1 and Statement 2 are false.
In the emission spectrum, a transition occurs from a higher energy state to a lower energy state—which corresponds to n(n-1)/2 transitions. However, this is not true for the absorption spectrum.
The spectrum from an H atom may be an emission spectrum or an absorption spectrum.
Question 8. Statement 1 The Bohr model cannot be used to explain multiple electron spectra.
Statement 2 It does not take interelectronic interactions into account.
Answer: 5. Both Statement 1 and Statement 2 are false.
Multiple electronic spectra can be explained for various transitions from a higher energy state to a lower energy state.
Question 9. Statement 1 Electrons in the atom are held due to Coulomb forces.
Statement 2 The atom is stable only because the centripetal force due to the Coulomb force is balanced by the centrifugal force.
Answer: 3. Statement 1 is true and Statement 2 is false.
An electrostatic attraction on the orbital electron provides the required centripetal force and keeps the atom stable, and the orbits are non-radiating (stationary).
Question 10. Statement 1 X-ray astronomy is possible only from the satellites orbiting the Earth.
Statement 2 The efficiency of an X-ray telescope is larger than compared to any other telescope.
Answer: 3. Statement 1 is true and Statement 2 is false.
X-rays are absorbed in the Earth’s atmosphere, so X-ray astronomy will not be suitable from the Earth but from its satellites, where there are no atmospheres.
Question 11. Statement 1 A fluorescent tube emits white light.
Statement 2 An emission of light in a fluorescent tube takes place at a very high temperature.
Answer: 5. Both Statement 1 and Statement 2 are false.
The light emitted by a fluorescent tube is of multiple colors depending on the nature of the gas enclosed. Thus, the emission occurs at the normal temperature.
The Nucleus Radioactivity
Question 1. Statement 1 Nuclei having a mass number around 60 are the most stable.
Statement 2 When two or more light nuclei are combined into a heavier nucleus, the binding energy per nucleon will increase.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
In the binding-energy (BE) curve, the peak is at around A = 60, for which BE/4 is the maximum. This corresponds to the most stable nuclei. In a fusion reaction, the resultant nucleus is more stable due to the increased binding energy.
Question 2. Statement 1 Mass defects in nuclear reactions are less than 1%.
Statement 2 In nuclear reactions, the change in binding energy per nucleon (BE/A) is generally less than 1%.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The increase in binding energy is due to the mass defect (BE = ΔMc2).
Question 3. Statement 1 Cobalt-60 is useful in cancer therapy.
Statement 2 Cobalt-60 is a source of γ – radiation, capable of killing cancerous cells.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Cobalt-60 \(\left({ }^{60} \mathrm{Co}\right)\) is a synthetic radioisotope of cobalt which is produced artificially in nuclear reactors. It is a source of γ-rays, which are used to kill cancerous cells.
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Question 4. Statement 1 Neutrons penetrate matter more readily as compared to protons.
Statement 2 Neutrons are slightly more massive than protons.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
“physics questions and answers “
A neutron has a charge and a mass slightly more than that of a proton. Being electrically neutral, it can penetrate matter more than an electron can.
Question 5. Statement 1 Radioactive nuclei emit β-particles.
Statement 2 Electrons exist inside the nucleus.
Answer: 3. Statement 1 is true and Statement 2 is false.
A nucleus is composed of protons and neutrons only. Emissions of β- particles are due to the conversion of a neutron into a proton:
\({ }_0^1 \mathrm{n} \rightarrow{ }_1^1 \mathrm{p}+{ }_{-1}^0 \mathrm{\beta}+\overline{\mathrm{v}}\)Question 6. Statement 1 The densities of all nuclei are the same.
Statement 2 The radius of a nucleus is directly proportional to the cube root of the mass number.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The density of a nucleus is constant (2.3 x l017 kg m-3) and is independent of the size of the nucleus. This follows from the condition
R = R0A1/3
Question 7. Statement 1 γ-radiation emissions occur after α- and β-decays.
Statement 2 Energy levels occur in a nucleus.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
After a β-emission, the daughter nucleus is left in an excited state. It de-excites itself with emissions of gamma rays. The same is true for an α-decay.
Thus, nuclei have discrete energy levels, and gamma-ray emissions occur due to transitions between these levels.
Question 8. Statement 1 Isotopes of an element can be separated by using a mass spectrometer.
Statement 2 Separation of isotopes is possible because of the difference in the electron numbers in the isotopes.
Answer: 3. Statement 1 is true and Statement 2 is false.
Isotopes of an element can be separated by mass spectrometers, in which electric and magnetic fields are used. Isotopes have the same number of protons but different numbers of neutrons.
Question 9. Statement 1 Heavy water is a better moderator than normal water.
Statement 2 Heavy water absorbs neutrons more efficiently than normal water.
Answer: 3. Statement 1 is true and Statement 2 is false.
Heavy water (D20) is used in nuclear reactors to slow down fast-moving neutrons by collisions so that they can produce fission reactions with U-235.
Question 10. Statement 1 For a nuclear reactor, it is desirable to have a multiplication factor of k = 1.
Statement 2 Sustained chain reactions occur in this critical condition.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
For controlled chain reactions, the multiplication factor is k= 1. For k >1, the chain reaction is uncontrolled, and an enormous amount of energy is released.
Question 11. Statement 1 The binding energy per nucleon for nuclei with atomic mass numbers A > 100 decreases with A.
Statement 2 The nuclear forces are weak for heavier nuclei.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
From the binding-energy curve, BE/A decreases with an increase in A for nuclei having A > 100. A decrease in BE indicates a decrease in stability and an increase in Coulomb repulsion between protons.
Question 12. Statement 1 A beam of charged particles is employed in the treatment of cancer.
Statement 2 Charged particles on passing through a material medium lose their energy by causing ionization of atoms along their paths.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
A beam of charged particles (protons) is used to treat cancer. During their passage to the target, they ionize the material medium.
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Question 13. Statement 1 In the process of nuclear fission, the fragments emit two or three neutrons as soon as they are formed, and they subsequently emit particles.
Statement 2 As the fragments contain an excess of neutrons over protons, emissions of neutrons and particles bring their neutron-proton ratios to stable values.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
In nuclear fission, a heavy nucleus breaks up into two lighter nuclei with emissions of 2-3 fast-moving neutrons. This emission is due to the comparatively larger value of the neutron-proton ratio in the products.
Question 14. Statement 1 Heavy water is preferred to ordinary water as a moderator in reactors.
Statement 2 Heavy water, used for slowing down the fast-moving neutrons, has a lesser absorption probability of neutrons than ordinary water.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Heavy water is a better moderator because, in addition to slowing down fast-moving neutrons, its absorption probability is comparatively less.
Question 15. Statement 1 The Rydberg constant varies as the mass number of a given element.
Statement 2 The reduced mass of the electron is dependent on the mass of the nucleus only.
Answer: 4. Statement 1 is false and Statement 2 is true.
The Rydberg constant (\(\left.R_{\infty}=m e^4 / 8 \varepsilon_0^2 h^3 c\right)\)) is independent of the mass number of a given element. The reduced mass for a heavy nucleus is
∴ \(\mu=\frac{m_{\mathrm{e}} M}{m_{\mathrm{e}}+M} \approx m e\)
Question 16. Statement 1 X-rays can penetrate through the flesh but not through the bones.
Statement 2 The penetrating power of X-rays depends on the accelerating voltage.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Bones are much harder than flesh. So, the X-rays can pass through the flesh but not through the bones. Higher accelerating voltages emit X-ray photons of higher energy, called hard X-rays.
Question 17. Statement 1 More energy is released in a fusion than in a fission.
Statement 2 More nucleons take part a fission.
Answer: 3. Statement 1 is true and Statement 2 is false.
A fusion reaction releases 3-4 times more energy than a fission reaction. The number of nuclei participating in a fusion is more than that in a fission.
Question 18. Statement 1 Generally, heavy nuclei are unstable.
Statement 2 It has more neutrons than protons.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Heavy nuclei are unstable and they decay, because they have less binding energy per nucleon. The neutron-proton ratio increases with an increase in mass number.
Question 19. Statement 1 Heavy water is used as a moderator in nuclear reactors.
Statement 2 Water cools down the fast neutrons.
Answer: 3. Statement 1 is true and Statement 2 is false.
Moderation is the process of the reduction of the initial high kinetic energy of fast neutrons during fission.
Since neutrons are light compared to most nuclei, the moderator must be such that it has a nearly identical mass.
This is achieved by heavy water (D20), which has a moderating efficiency of 80 times that of ordinary water.
Question 20. Statement 1 Thermonuclear fusion reactions may become sources of unlimited power for mankind.
Statement 2 A single fusion event involving isotopes of hydrogen produces more energy than the energy from the nuclear fission of \({ }_{92}^{235} \mathrm{U}\).
Answer: 3. Statement 1 is true and Statement 2 is false.
In a fusion reaction, light nuclei (like H2) fuse together with a release of clean energy suitable for mankind.
One fusion event produces less energy compared to that produced in a single fission.
Question 21. Statement 1 If a heavy nucleus is split up into two medium-sized parts, each of the nuclei will have more binding energy per nucleon than the original nucleus.
Statement 2 Joining two lighter nuclei together to form a single nucleus of medium size means more binding energy per nucleon than the two light nuclei.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Heavy nuclei are less stable and have a lower value of BE/A. They break up so that the lighter nuclei are more stable with greater values of BE/A.
From the binding-energy curve, lighter nuclei have less binding energy and hence are unstable. When they fuse to form medium-sized nuclei, they become more stable and have a higher binding energy.
Question 22. Statement 1 It is desirable to slow down fast-moving neutrons to sustain controlled chain reactions.
Statement 2 Slow-moving neutrons efficiently collide with \({ }^{235} \mathrm{U}\) nuclei.
Answer: 3. Statement 1 is true and Statement 2 is false.
Fast neutrons are produced during nuclear fission. A fission of \({ }^{235} \mathrm{U}\) is possible with thermal neutrons. So, for a sustained reaction, neutrons are slowed down by moderators.
Question 23. Statement 1 \({ }^{90} \mathrm{Sr}\) from the radioactive fallout from a nuclear explosion ends up in the bones of human beings through the milk consumed by them. It leads to an impaired production of red blood cells.
Statement 2 The energetic β-particles emitted in the decay of \({ }^{90} \mathrm{Sr}\) damage the bone marrow.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Strontium-90 is a radioactive isotope produced by nuclear fission. It undergoes a β-decay into yttrium-90 with a decay energy of 0.546 MeV.
Strontium-90 gets deposited in our bones and bone marrow. Its presence in the bones can cause bone cancer.
“physics questions and answers “
Question 24. Statement 1 It is very easy to detect neutrinos in nature.
Statement 2 It has a high affinity to interact with matter.
Answer: 5. Both Statement 1 and Statement 2 are false.
A neutrino is a subatomic elementary particle with no electric charge and very little mass (≈ 0.2 x 10-5 x me). They are most penetrating and capable of passing through an enormous number of atoms without causing any reaction.
Hence, neutrinos are very difficult to defect and have an extremely low affinity to interact with matter.
Question 25. Statement 1 \({ }_{27}^{60} \mathrm{Co}\) is a source of gamma radiation.
Statement 2 Gamma emissions are due to nuclear decay.
Answer: 3. Statement 1 is true and Statement 2 is false.
Cobalt-60 is a radioactive isotope and a source of gamma radiation, used to destroy tumors.
A nucleus has discrete energy levels and transitions from higher to lower energy levels to emit γ-rays.
Question 26. Statement 1 Magnetic resonance imaging (MRI) is a useful diagnostic tool for producing images of various parts of the human body.
Statement 2 Protons in various tissues of the human body play a role in MRI.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
MRI is a medical imaging technique used in radiology to produce images of various parts of the human body. The human body is mostly composed of water, which contains hydrogen nuclei (protons). These nuclei play a significant role in the MRI process.
Question 27. Statement 1 A radium nucleus at rest decayed into of nucleus and an α-particle. They both move back to each other.
Statement 2 law of conservation of linear momentum.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
Radium-226 decays into radon-222 through an alpha emission. It follows from the principle of conservation of linear momentum that both the products must move in opposite directions with equal momenta.
Question 28. Statement 1 The ratio of the time taken for light emissions from an atom to that for the release of nuclear energy in a fission is 1: 100.
Statement 2 The time taken for the light emission from an atom is of the order of 10-8 s.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The time taken for a light emission from an atom is around 10-8 seconds. The time taken for the release of energy during a fission reaction is around 10-6 s.
∴ required ratio = \(\frac{10^{-8} s}{10^{-6} s}=\frac{1}{100}\)
Question 29. Statement 1 The number of active nuclei present in a radioactive sample decreases exponentially with time.
Statement 2 The activity of a radioactive sample decreases linearly with time.
Answer: 3. Statement 1 is true and Statement 2 is false.
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According to the law of radioactive disintegration, \(-\frac{d N}{d t}=\lambda N\), which leads to \(N=N_0 \mathrm{e}^{-\lambda t}\). Thus, the number of active nuclei decreases exponentially with time.
Activity = \(|A|=\left|\frac{d N}{d t}\right|=\lambda N=\lambda N_0 \mathrm{e}^{-\lambda t}=A_0 \mathrm{e}^{-\lambda t}\),
which decreases exponentially with time.
Question 30. Statement 1 When a- and β-particles pass through external electric fields, β-particles are deflected much more than a-particles.
Statement 2 β-particles have much larger velocities than a-particles.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Force = F = qE and acceleration = \(a=\frac{q E}{m}\)
Let the particles enter the electric field perpendicularly so that the displacement along the field be
⇒ \(y=\frac{1}{2} a t^2=\frac{1}{2}\left(\frac{q E}{m}\right) t^2\)
∴\(\frac{y_{\mathrm{e}}}{y_\alpha}=\frac{m_\alpha e}{2 e m_{\mathrm{e}}}=\frac{m_\alpha}{2 m_{\mathrm{e}}} \gg 1\)
∴ Hence, \(y_{\mathrm{e}} \gg y_\alpha\)
Question 31. Statement 1 In an X-ray tube, the wavelength of the characteristic X-rays depends on the metal used as the target.
Statement 2 Metals of large atomic numbers are best suited for the production of X-rays.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Characteristic X-rays are emitted due to transitions of electrons from the outer shell to a vacancy in the inner shell of an atom. These X-rays are characteristics of the target element and vary with the metal used. Tungsten (an element of a high atomic number) is most commonly used in an X-ray tube as the target because its melting point is high.
Question 32. Statement 1 Characteristic X-rays are produced by transitions of orbital electrons in the target atom.
Statement 2 In characteristic X-rays, Kα X-rays are of a smaller wavelength than that of Kβ X-rays for the same element.
Answer: 3. Statement 1 is true and Statement 2 is false.
Characteristic X-rays correspond to transitions of electrons from higher-energy shells to lower-energy shells.
The wavelength of characteristic X-rays depends on the difference in energy in the two shells.
For \(\mathrm{K}_\alpha, \lambda=\frac{h c}{E_{\mathrm{K}}-E_{\mathrm{L}}}\)
For \(\mathrm{K}_\beta, \lambda=\frac{h c}{E_{\mathrm{K}}-E_{\mathrm{M}}}\)
∵ \(\Delta E_{\mathrm{KL}}<\Delta E_{\mathrm{KM}}\)
∴ \(\lambda_{\mathrm{K} \alpha}>\lambda_{\mathrm{K} \beta}\)
So, the reason is false.
Question 33. Statement 1 In radioactivity, the nature of a sample is identified by its half-life or by its average life but not by its total life.
Statement 2 The total life of any radioactive sample is infinity.
Answer: 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
The half-life and mean life are characteristics of the radioactive sample but the total life for any such sample is infinity. Since the decay is exponential, the number of active nuclei will reduce to zero after an infinite time.
Question 34. Statement 1 If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change.
Statement 2 When an electron beam strikes the target in an X-ray tube, part of its kinetic energy is converted into X-ray energy.
Answer: 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
Emissions of characteristic X-rays are due to electronic transitions from higher-energy shells to lower-energy shells, in which the energy values are fixed, discrete, and thus independent of accelerating potential.
X-rays are produced due to sudden decelerations of fast-moving electrons when they collide and interact with the target (anode). Only 1% of the KE of electrons is converted into X-rays and the rest into heat.