Modern Physics — CBSE Class 12 board PYQs

The potential energy between two nucleons inside a nucleus is minimum at a distance of about

The variation of the stopping potential $V_0$ with the frequency $\nu$ of the incident radiation for four metals A, B, C and D is shown in the figure. For the same frequency of incident radiation producing photo-electrons in all metals, the kinetic energy of photo-electrons will …

The energy of an electron in the ground state of a hydrogen atom is $-13.6$ eV. The kinetic and potential energy of the electron in the first excited state will be

Assertion (A): An alpha particle is moving towards a gold nucleus. The impact parameter is maximum for the scattering angle of $180^{\circ }$.
Reason (R): The impact parameter in an alpha particle scattering experiment does not depend upon the atomic number of the target nucleus.

Which one of the following metals does not exhibit emission of electrons from its surface when irradiated by visible light?

A hydrogen atom makes a transition from $n=5$ to $n=1$ orbit. The wavelength of the photon emitted is $\lambda$. The wavelength of the photon emitted when it makes a transition from $n=5$ to $n=2$ orbit is

The curve of binding energy per nucleon as a function of atomic mass number has a sharp peak for the helium nucleus. This implies that the helium nucleus is

Which of the following statements is not correct according to the Rutherford model?

Photons of energies 1 eV and 2 eV are successively incident on a metallic surface of work function 0.5 eV. The ratio of kinetic energy of most energetic photoelectrons in the two cases will be:

According to Bohr's atomic model, the circumference of the electron orbit is always an ____ multiple of the de-Broglie wavelength.

In $\beta$-decay, the parent and daughter nuclei have the same number of ____.

The nuclear radius of ${}_{13}^{27}\mathrm{Al}$ is 3.6 fermi. Find the nuclear radius of ${}_{29}^{64}\mathrm{Cu}$.

A proton and an electron have equal speeds. Find the ratio of the de-Broglie wavelengths associated with them.

The variation of the stopping potential $V_0$ with the frequency $\nu$ of the light incident on two different photosensitive surfaces $M_1$ and $M_2$ is shown in the figure. Identify the surface which has the greater value of work function.

Define the term "threshold frequency" in the context of photoelectric emission.

Define the term "Intensity" in the photon picture of electromagnetic radiation.

Draw graphs showing the variation of photoelectric current with applied voltage for two incident radiations of equal frequency and different intensities. Mark the graph for the radiation of higher intensity.

Four nuclei of an element undergo fusion to form a heavier nucleus, with release of energy. Which of the two — the parent or the daughter nucleus — would have higher binding energy per nucleon?

State one factor which determines the intensity of light in the photon picture of light.

The graph shows the variation of stopping potential $V_0$ versus frequency of incident radiation $\nu$ for two photosensitive metals A and B. Which of the two metals has the higher threshold frequency and why?

Why is it found experimentally difficult to detect neutrinos in nuclear $\beta$-decay?

Write the expression for the de-Broglie wavelength associated with a charged particle having charge $q$ and mass $m$, when it is accelerated by a potential $V$.

Define the activity of a given radioactive substance. Write its S.I. unit.

State de-Broglie hypothesis.

Write any two characteristic properties of nuclear force.

Write the expression for Bohr's radius in a hydrogen atom.

The radius of the innermost electron orbit of a hydrogen atom is $5.3\times 10^{-11}\text{m}$. What is the radius of the orbit in the second excited state?

Two nuclei have mass numbers in the ratio $1:2$. What is the ratio of their nuclear densities?

Two nuclei have mass numbers in the ratio $8:125$. What is the ratio of their nuclear radii?

The maximum kinetic energy of a photoelectron is 3 eV. What is its stopping potential?

The figure shows a plot of three curves a, b, c showing the variation of photocurrent vs collector plate potential for three different intensities $I_1$, $I_2$ and $I_3$ having frequencies ${\nu }_1$, ${\nu }_2$ and ${\nu }_3$ respectively incident on a photosensitive surface. Point out t …

What is the stopping potential of a photocell in which electrons with maximum kinetic energy of 6 eV are emitted?

What is the nuclear radius of ${}^{125}\mathrm{Te}$, if that of ${}^{27}\mathrm{Al}$ is 3.6 fermi?

An electron, an alpha-particle and a proton have the same kinetic energy. Which one of these particles has the largest de-Broglie wavelength?

The radioactive isotope D decays according to the sequence $\mathrm{D}\stackrel{{\beta }^{-}}{\to }{\mathrm{D}}_1\stackrel{\alpha }{\to }{\mathrm{D}}_2$. If the mass number and atomic number of ${\mathrm{D}}_2$ are 176 and 71 respectively, what is
(i) the mass number of D,
(ii) t …

The de-Broglie wavelength associated with an electron accelerated through a potential difference $V$ is $\lambda$. What will be its wavelength when the accelerating potential is increased to $4V$?

Ultraviolet light is incident on two photosensitive materials having work functions $W_1$ and $W_2$ $(W_1>W_2)$. In which case will the kinetic energy of the emitted electrons be greater? Why?

Two metals A and B have work functions 4 eV and 10 eV respectively. Which metal has higher threshold wavelength?

Calculate the energy released / absorbed (in MeV) in the nuclear reaction ${}_1^1\mathrm{H}+{}_1^3\mathrm{H}\to {}_1^2\mathrm{H}+{}_1^2\mathrm{H}$. Given $m{(}_1^1\mathrm{H})=1.007825u$, $m{(}_1^2\mathrm{H})=2.014102u$, …

A proton of energy 1.6 MeV approaches a gold nucleus $(Z=79)$. Find the distance of its closest approach.

A photosensitive surface of work function 2.1 eV is irradiated by radiation of wavelength 150 nm. Calculate
(i) the threshold wavelength,
(ii) the energy (in eV) of an incident photon, and
(iii) the maximum kinetic energy of the emitted photoelectron.

How are X-rays produced? Give any two uses of these.

What is meant by ionization energy? Write its value for the hydrogen atom.

Define the term mass defect. How is it related to the stability of the nucleus?

(a)(i) Distinguish between nuclear fission and fusion, giving an example of each. (ii) Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon.

(b)(i) How is the size of a nucleus found experimentally? Write the relation between the radius and the mass number of a nucleus. (ii) Prove that the density of a nucleus is independent of its mass number.

What results do you expect if the $\alpha$-particle scattering experiment is repeated using a thin sheet of hydrogen in place of a gold foil? Explain. (Hydrogen is a solid at a temperature below 14 K.)

Why is it the frequency and not the intensity of the light source that determines whether emission of photoelectrons will occur or not? Explain.

An alpha particle is accelerated through a potential difference of 100 V. Calculate (i) the speed acquired by the alpha particle and (ii) the de-Broglie wavelength associated with it. (Take mass of alpha particle $=6.4\times 10^{-27}\mathrm{kg}$.)

(a) Use Bohr's postulate to prove that the radius of the $n^{\text{th}}$ orbit in a hydrogen atom is proportional to $n^2$.
(b) How will the energy of a hydrogen atom change if $n$ increases from 1 to $\infty$?

In a fission event of ${}_{92}^{238}\mathrm{U}$ by fast moving neutrons, no neutrons are emitted and the final products, after the beta decay of the primary fragments, are ${}_{58}^{140}\mathrm{Ce}$ and ${}_{44}^{99}\mathrm{Ru}$. Calculate $Q$ for this process. Neglect the masses of th …

Define the term 'half-life' of a radioactive substance. Two different radioactive substances have half-lives $T_1$ and $T_2$ and the number of undecayed atoms at an instant are $N_1$ and $N_2$ respectively. Find the ratio of their activities at that instant.

Using Bohr's atomic model, derive the expression for the radius of the $n^{\text{th}}$ orbit of the revolving electron in a hydrogen atom.

(a) Write two main observations of the photoelectric effect experiment which could only be explained by Einstein's photoelectric equation.
(b) Draw a graph showing the variation of photocurrent with the anode potential of a photocell.

The nucleus ${}_{92}^{235}\mathrm{Y}$, initially at rest, decays into ${}_{90}^{231}\mathrm{X}$ by $\alpha$-emission: ${}_{92}^{235}\mathrm{Y}\to {}_{90}^{231}\mathrm{X}+{}_2^4\mathrm{He}+\text{energy}$. The binding energies per nucleon of the parent nucleus, the daughte …

(a) Define the terms (i) threshold frequency and (ii) stopping potential in the photoelectric effect. (b) Plot a graph of photocurrent versus anode potential for radiation of frequency $\nu$ and intensities $I_1$ and $I_2$ $(I_1<I_2)$.

State Bohr's quantization condition of angular momentum. Calculate the shortest wavelength of the Brackett series and state to which part of the electromagnetic spectrum it belongs.

Calculate the orbital period of the electron in the first excited state of a hydrogen atom.

Why is the wave theory of electromagnetic radiation not able to explain the photoelectric effect? How does the photon picture resolve this problem?

Obtain the expression for the ratio of the de-Broglie wavelengths associated with the electron orbiting in the second and third excited states of a hydrogen atom.

(a) Explain briefly how Rutherford scattering of $\alpha$-particles by a target nucleus can provide information on the size of the nucleus.
(b) Show that the density of a nucleus is independent of its mass number $A$.

If light of wavelength 412.5 nm is incident on each of the metals given below, which ones will show photoelectric emission and why? (Na: 1.92 eV; K: 2.15 eV; Ca: 3.20 eV; Mo: 4.17 eV.)

(a) State Bohr's postulate to define stable orbits in a hydrogen atom. How does de-Broglie's hypothesis explain the stability of these orbits?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the $n=4$ level. Estimate the frequency of the pho …

(a) Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon (BE/A) versus the mass number $A$.
(b) A radioactive isotope has a half-life of 10 years. How long will it take for the activity to reduce to 3.12%?

Calculate the shortest wavelength of light emitted in the Paschen series of the hydrogen spectrum. Which part of the electromagnetic spectrum does it belong to? (Given: Rydberg constant $R=1.1\times 10^7{\mathrm{m}}^{-1}$.)

Find the wavelength of the electron orbiting in the first excited state in a hydrogen atom.

Define the distance of closest approach. An $\alpha$-particle of kinetic energy $K$ is bombarded on a thin gold foil. The distance of closest approach is $r$. What will be the distance of closest approach for an $\alpha$-particle of double the kinetic energy?

Write two important limitations of the Rutherford nuclear model of the atom.

Draw a graph showing the variation of de-Broglie wavelength of a particle of charge $q$ and mass $m$ with the accelerating potential. A proton and a deuteron have the same de-Broglie wavelengths. Explain which has more kinetic energy.

In the study of the photoelectric effect, the graph between the stopping potential $V$ and frequency $\nu$ of the incident radiation on two different metals P and Q is shown.
(i) Which one of the two metals has the higher threshold frequency?
(ii) Determine the work function of t …

(i) A radioactive nucleus 'A' undergoes a series of decays as given below: $A\stackrel{\alpha }{\to }{A}_1\stackrel{\beta }{\to }{A}_2\stackrel{\alpha }{\to }{A}_3\stackrel{\gamma }{\to }{A}_4$. The mass number and atomic number of $A_2$ are 176 and 71 respectively. Determine the …

Plot a graph showing the variation of de-Broglie wavelength $\lambda$ versus $\frac{1}{\sqrt{V}}$, where $V$ is the accelerating potential, for two particles A and B carrying the same charge but of masses $m_1$ and $m_2$ $(m_1>m_2)$. Which one of the two represents a particle …

Calculate the energy in the fusion reaction ${}_1^2\mathrm{H}+{}_1^2\mathrm{H}\to {}_2^3\mathrm{He}+n$, where the binding energy of ${}_1^2\mathrm{H}=2.23\mathrm{MeV}$ and of ${}_2^3\mathrm{He}=7.73\mathrm{MeV}$.

A proton and an $\alpha$-particle are accelerated through the same potential difference. Which one of the two has
(i) the greater de-Broglie wavelength, and
(ii) less kinetic energy? Justify your answer.

When is the $H_{\alpha }$ line in the emission spectrum of a hydrogen atom obtained? Calculate the frequency of the photon emitted during this transition.

Calculate the wavelength of the radiation emitted when the electron in a hydrogen atom jumps from $n=\infty$ to $n=1$.

State two important properties of the photon which are used to write Einstein's photoelectric equation. Define
(i) stopping potential and
(ii) threshold frequency, using Einstein's equation and drawing the necessary plot between relevant quantities.

(i) Derive the mathematical expression for the law of radioactive decay for a sample of radioactive nuclei.
(ii) How is the mean life of a given radioactive nucleus related to the decay constant?

Write three characteristic features in the photoelectric effect which cannot be explained on the basis of the wave theory of light but can be explained only using Einstein's equation.

(i) State Bohr's quantization condition for defining stationary orbits. How does the de-Broglie hypothesis explain the stationary orbits?
(ii) Find the relation between the three wavelengths ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$ from the energy level diagram shown.

A proton and an $\alpha$-particle have the same de-Broglie wavelength. Determine the ratio of
(i) their accelerating potentials,
(ii) their speeds.

Show that the radius of the orbit in a hydrogen atom varies as $n^2$, where $n$ is the principal quantum number of the atom.

Write Einstein's photoelectric equation and mention which important features in the photoelectric effect can be explained with the help of this equation. The maximum kinetic energy of the photoelectrons gets doubled when the wavelength of light incident on the surface changes fro …

In the study of the Geiger-Marsden experiment on scattering of $\alpha$-particles by a thin foil of gold, draw the trajectory of $\alpha$-particles in the Coulomb field of the target nucleus. Explain briefly how one gets information on the size of the nucleus from this study. Fro …

Distinguish between nuclear fission and fusion. Show how in both these processes energy is released. Calculate the energy released in MeV in the deuterium-tritium fusion reaction ${}_1^2\mathrm{H}+{}_1^3\mathrm{H}\to {}_2^4\mathrm{He}+n$ using the data …

Using the Rutherford model of the atom, derive the expression for the total energy of the electron in a hydrogen atom. What is the significance of the total negative energy possessed by the electron?

Using Bohr's postulates of the atomic model, derive the expression for the radius of the $n^{\text{th}}$ electron orbit. Hence obtain the expression for Bohr's radius.

An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie wavelength associated with the electrons. Taking other factors, such as numerical aperture etc., to be the same, how does the resolving power of an electron microscope compare with t …

For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents that they get a medical check-up of …

Write Einstein's photoelectric equation and point out any two characteristic properties of photons on which this equation is based. Briefly explain the three observed features which can be explained by this equation.

Write Einstein's photoelectric equation. State clearly how this equation is obtained using the photon picture of electromagnetic radiation. Write the three salient features observed in the photoelectric effect which can be explained using this equation.

(a) Using Bohr's second postulate of quantization of orbital angular momentum, show that the circumference of the electron in the $n^{\text{th}}$ orbital state in a hydrogen atom is $n$ times the de-Broglie wavelength associated with it.
(b) The electron in a hydrogen atom is ini …

(i) What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number $A$ lying $30<A<170$?
(ii) Show that the density of a nucleus over a wide range of nuclei is constant — independent of mass number $A$.

Define the term 'stopping potential' in relation to the photoelectric effect.

Draw a plot showing the variation of photoelectric current with collector plate potential for two different frequencies ${\nu }_1>{\nu }_2$ of incident radiation having the same intensity. In which case will the stopping potential be higher? Justify your answer.

(a) Using de-Broglie's hypothesis, explain with the help of a suitable diagram Bohr's second postulate of quantization of orbital angular momentum in a hydrogen atom.
(b) The ground state energy of a hydrogen atom is $-13.6$ eV. What are the kinetic and potential energies of the …

An electron is accelerated through a potential difference of 64 volts. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond?

Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work functions $W_1$ and $W_2$ $(W_1>W_2)$. On what factors do the
(i) slope and
(ii) intercept of the lines depend?

A heavy nucleus $X$ of mass number 240 and binding energy per nucleon 7.6 MeV is split into two fragments $Y$ and $Z$ of mass numbers 110 and 130. The binding energy of nucleons in $Y$ and $Z$ is 8.5 MeV per nucleon. Calculate the energy $Q$ released per fission in MeV.

(i) Define 'activity' of a radioactive material and write its S.I. unit.
(ii) Plot a graph showing the variation of activity of a given radioactive sample with time.

A radioactive nucleus 'A' undergoes a series of decays according to the following scheme: $A\stackrel{\alpha }{\to }{A}_1\stackrel{{\beta }^{-}}{\to }{A}_2\stackrel{\alpha }{\to }{A}_3\stackrel{\gamma }{\to }{A}_4$. The mass number and atomic number of $A$ are 180 and 72 respective …

An electron and a proton are accelerated through the same potential. Which one of the two has
(i) the greater value of de-Broglie wavelength associated with it, and
(ii) less momentum? Justify your answer.

(a) The energy levels of an atom are as shown in the figure. Which of the transitions shown will result in the emission of a photon of wavelength 275 nm?
(b) Which transition corresponds to the emission of radiation of maximum wavelength?

Calculate the energy released in MeV in the following nuclear reaction: ${}_{92}^{238}\mathrm{U}\to {}_{90}^{234}\mathrm{Th}+{}_2^4\mathrm{He}+Q$. [Mass of ${}_{92}^{238}\mathrm{U}=238.05079u$; mass of ${}_{90}^{234}\mathrm{Th}=234.043630u$; mass of …

Distinguish between isotopes and isobars. Give one example for each species. A radioactive isotope has a half-life of 5 years. How long will it take for the activity to reduce to 3.125%?

Draw a plot of the potential energy of a pair of nucleons as a function of their separation. What is the significance of the negative potential energy in the graph drawn?

Calculate the amount of energy released during the $\alpha$-decay ${}_{92}^{238}\mathrm{U}\to {}_{90}^{234}\mathrm{Th}+{}_2^4\mathrm{He}$. Given: atomic mass of ${}_{92}^{238}\mathrm{U}=238.05079u$, ${}_{90}^{234}\mathrm{Th}=234.04363u$, …

In a plot of photoelectric current versus anode potential, how does
(i) the saturation current vary with anode potential for incident radiations of different frequencies but the same intensity,
(ii) the stopping potential vary for incident radiations of different intensities but …

Define the terms threshold frequency and stopping potential in relation to the phenomenon of the photoelectric effect. How is the photoelectric current affected on increasing the
(i) frequency,
(ii) intensity of the incident radiation, and why?

Sketch a graph between the frequency of incident radiation and the stopping potential for a given photosensitive material. What information can be obtained from the value of the intercept on the potential axis? A source of light of frequency greater than the threshold frequency i …

Define the terms half-life period and decay constant of a radioactive substance. Write their S.I. units. Establish the relationship between the two.

A neutron is absorbed by a ${}_3^6\mathrm{Li}$ nucleus with the subsequent emission of an alpha particle.
(i) Write the corresponding nuclear reaction.
(ii) Calculate the energy released, in MeV. Given: mass ${}_3^6\mathrm{Li}=6.015126u$; mass (neutron) $=1.0086654u$; …

(a) Draw the energy level diagram showing the emission of $\beta$-particles followed by $\gamma$-rays by a ${}_{27}^{60}\mathrm{Co}$ nucleus.
(b) Plot the distribution of kinetic energy of $\beta$-particles and state why the energy spectrum is continuous.

A radioactive sample contains 2.2 mg of pure ${}_6^{11}\mathrm{C}$, which has a half-life period of 1224 seconds. Calculate:
(i) the number of atoms present initially;
(ii) the activity when 5 $\mu$g of the sample is left.

Mention the significance of the Davisson-Germer experiment. An $\alpha$-particle and a proton are accelerated from rest through the same potential difference $V$. Find the ratio of the de-Broglie wavelengths associated with them.

The half-life of ${}_{92}^{238}\mathrm{U}$ against $\alpha$-decay is $4.5\times 10^9$ years. Calculate the activity of a 1 g sample of ${}_{92}^{238}\mathrm{U}$.

Red light, however bright, cannot produce the emission of electrons from a clean zinc surface, but even weak ultraviolet radiation can do so. Why? X-rays of wavelength $\lambda$ fall on a photosensitive surface, emitting electrons. Assuming that the work function of the surface c …

Define the terms 'half-life period' and 'decay constant' of a radioactive sample. Derive the relation between these terms.

When a deuteron of mass $2.0141u$ and negligible kinetic energy is absorbed by a lithium (${}_3^6\mathrm{Li}$) nucleus of mass $6.0155u$, the compound nucleus disintegrates spontaneously into two alpha particles, each of mass $4.0026u$. Calculate the energy in joules carr …

Calculate the binding energy per nucleon of the ${}_{20}^{40}\mathrm{Ca}$ nucleus. [Given: $m{(}_{20}^{40}\mathrm{Ca})=40.078u$; $m_n=1.008665u$; $m_p=1.007825u$.]

Calculate the binding energy per nucleon of the iron nucleus. [Given: mass of ${}_{26}^{56}\mathrm{Fe}=55.934939u$; mass of a neutron $=1.008665u$; mass of a proton $=1.007825u$.]

Explain with an example whether the neutron-proton ratio in a nucleus increases or decreases due to beta ($\beta$) decay.

Derive the expression for the de-Broglie wavelength of an electron moving under a potential difference of $V$ volts. Describe the Davisson and Germer experiment to establish the wave nature of electrons. Draw a labelled diagram of the apparatus used.

(a) The figure shows the variation of photoelectric current measured in a photo-cell circuit as a function of the potential difference between the plates of the photo-cell when light beams A, B, C and D of different wavelengths are incident on the photo-cell. Examine the figure a …

What is the effect on the threshold frequency and the stopping potential on increasing the frequency of the incident beam of light? Justify your answer.

Using Bohr's postulates, derive the expression for the frequency of radiation emitted when the electron in a hydrogen atom undergoes a transition from a higher energy state (quantum number $n_i$) to a lower state ($n_f$). When the electron in a hydrogen atom jumps from energy sta …

(a) Draw the plot of binding energy per nucleon (BE/A) as a function of mass number $A$. Write two important conclusions that can be drawn regarding the nature of the nuclear force.
(b) Use this graph to explain the release of energy in both the processes of nuclear fusion and fi …