# Modern Physics | Question Bank for Class 12 Physics

JEE Mains & AdvancedGet important questions of Modern Physics Class 12 for Boards exams. Download or View the Physics Question Bank Class 12. These important questions will play significant role in clearing concepts of Physics. This question bank is designed by NCERT keeping in mind and the questions are updated with respect to upcoming Board exams. You will get here all the important questions for class 12 Physics chapter wise CBSE. **Click Here for Detailed Chapter-wise Notes of PHYSICS for Class 12th, JEE & NEET.**

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**Q. Does the stopping potential in photoelectric emission depend upon (i) the intensity of the incident radiation in a photocell ? (ii) The frequency of the incident radiation ?**

**Q. Show graphically, how the stopping potential for a given photosensitive surface varies with the frequency. Mark threshold frequency on this graph**

**Q. Plot a graph showing the variation of photoelectric current with anode potential for two light beam of same wavelength but different intentisy**

**Q. With what purpose was famous Davisson-Germer experiment with the electrons performed ?**

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

**Q. In an experiment on photoelectric effect, the slope of the cut off voltage versus frequency of incident light is found to be $4.12 \times 10^{-15} \mathrm{Vs}$ Given $e=1.6 \times 10^{-19} \mathrm{C}$ estimate the value of Planck’s constant.**[NCERT]

**Q. The threshold frequency of a certain metal is $3.3 \times 10^{14} \mathrm{Hz}$ If light of frequency $8.2 \times 10^{14} \mathrm{Hz}$, is incident on the metal, predict the cut off voltage for photoelectric emission. Given plank’s constant $h=6.62 \times 10^{-34} \mathrm{J}$**[NCERT]

**Q. The threshold frequency of a metal is f0. When the light of frequency 2f0 is incident on the metal plate the maximum velocity of electrons emitted is v1. When the frequency of the incident radiation is increased to 5f0, the maximum velocity of electrons emitted is v2. Find the ratio of v1 and v2.**

**By using $E=W_{0}+K_{\max } \Rightarrow K_{\max }=E-W_{0}$**

**Where**

**Q. Given below is the graph between frequency () of the incident light and maximum kinetic energy(Ek) of emitted photoelectrons. Find the values of (i). Threshold frequency, and (ii) Work function from the graph**

**Q. The energy flux of sunlight reaching the surface of the earth is $1.388 \times 10^{3} \mathrm{W} / \mathrm{m}^{2}$. How many photons (nearly) per square metre are incident on the earth per second ? Assume that the photons in the sunlight have an average wavelength of 550 nm**[NCERT]

**Q. Find the (a) maximum frequency and (b) minimum wave length of X-rays produced by 30 kV electrons**[NCERT]

**Q. The work function of cesium metal is 2.14 eV. When light of frequency $6 \times 10^{14} \mathrm{Hz}$ is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons (b) Stopping potential and (c) Maximum speed of the emitted photoelectrons. Given $h=6.63 \times 10^{-34} \mathrm{Js}, \quad 1 e V=1.6 \times 10^{-19} \mathrm{J}, \mathrm{c}=3 \times 10^{8} \mathrm{m} / \mathrm{s}$ ,**[NCERT]

**Q. A 100 W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm. (a) What is energy associated per photon with the sodium light (b) At what rate are the photons delivered to the sphere ?**[NCERT]

**Q. The work unction for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm? Given, charge on electron,**

**$e=1.6 \times 10^{-19} \mathrm{C}, \quad c=3 \times 10^{8} \mathrm{m} / \mathrm{s} ; h=6.62 \times 10^{-34} \mathrm{Js}$**

**Q. Light of frequency $7.21 \times 10^{14} \mathrm{Hz}$ is incident on a metal surface. Electrons with a maximum speed of $6.0 \times 10^{5} \mathrm{ms}^{-1}$ are ejected from the surface. What is the threshold frequency for photoemission of electrons ? $h=6.63 \times 10^{-34} \mathrm{Js}$ and $m_{e}=9.1 \times 10^{-31} \mathrm{kg}$**[NCERT]

**Q. Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the cathode, the stopping potential of photoelectrons is 0.38 eV. Find the work function of the material from which the cathode is made. Given $h=6.63 \times 10^{-34} \mathrm{Js}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{J}$**[NCERT]

**Q. Calculate the (a) momentum and (b) de-Broglie wavelength of the electrons accelerated through a potential difference of 56 V.**

**Given; $h=6.63 \times 10^{-34} \mathrm{Js}, m_{e}=9 \times 10^{-31} \mathrm{kg}$ ;**

**Q. The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which (a) an electron (b) a neutron, would have the same de-Broglie wavelength**

**$h=6.6 \times 10^{-34} \mathrm{Js}, m_{e}=9 \times 10^{-31} \mathrm{kg} ; m_{n}=1.66 \times 10^{-27} \mathrm{kg}$**[NCERT]

**[question**

**] An electron and a photon each have a wavelength of 1.00 nm. Find (a) Their momenta (b) The energy of the photon and (c) The kinetic energy of electron $h=6.63 \times 10^{-34} \mathrm{Js}, \quad m_{e}=9 \times 10^{-31} \mathrm{kg}$**[NCERT]

**Q. (a) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at $0.45 \mathrm{A}$ What is the maximum energy of a photon in the radiation ?**

**(b) From answer to (a), give what order of accelerating voltage (for electrons) is required in such a tube.**[NCERT]

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**Q. An electron and a proton are possessing same amount of kinetic energy which of the two have greater de-Broglie wavelength ? Justify your answer**

**Q. Define the terms (i) work function (ii) threshold frequency and (iii) stopping potential, with reference to photoelectric effect**

**Q. X-rays of wavelength $\lambda$ fall on a photosensitive surface, emitting photoelectrons. Assuming X-rays of wavelength $\lambda$ fall on a photosensitive surface, emitting electrons. Assuming that the work function of the surface can be neglected, prove that the de- Broglie wavelength of electrons emitted will be $\sqrt{\frac{h \lambda}{2 m c}}$**

**Q.**

**The wavelength of a photon and the de-Broglie wavelength of an electron have the same value. Show that the energy of the photon is $\frac{2 \lambda m c}{h}$ times the kinetic energy of the electron, where m, c and h have their usual meanings.**

**Ans.**Kinetic energy of electron, $E_{K}=\frac{1}{2} \frac{m^{2} v^{2}}{m}=\frac{1}{2} \frac{h^{2}}{m \lambda 2}$ $\left[\because \lambda=\frac{h}{m v}\right]$ Energy of a photon, $E=\frac{h c}{\lambda}$

**Q. Quarks inside protons and neutrons are thought to carry fractional charges Why do they not show up in Milikan’s oil drop experiment ?**[NCERT]

**Q. Sketch the graphs, showing the variation of stopping potential with frequency of incident radiations for two photosensitive materials A and B having threshold frequencies $v_{0}>v_{0}$respectively.**

**(i) Which of the two metals, A or B has higher work function ?**

**(ii) Which in formation do you get from the slope of the graphs ?**

**(ii) What does the value of the intercept of graph A on the potential axis represent ?**

**Q. Draw the graphs showing the variation of photoelectric current with anode potential of a photocell for (i) The same frequencies but different intensities $I_{1}>I_{2}>I_{3}$ of incident radiations (ii) The same intensity but different frequencies $v_{1}>v_{2}>v_{3}$**

**of incident radiations**

**Q. What is the de-Broglie wavelength of**

**(a) a bullet of mass 0.40 kg travelling at a speed of $1.0 \mathrm{kms}^{-1}$**

**(b) a ball of mass 0.60 kg moving at a speed of 1.0 $m s^{-1}$ and**

**(c) a dust particle of mass $1.0 \times 10^{-9} \mathrm{kg}$ drifting**

**with a speed of $2.2 \mathrm{ms}^{-1} ? h=6.63 \times 10^{-34} \mathrm{J} \mathrm{s}$**[NCERT]

**Q. (a) For what kinetic energy of a neutron will the associated de-Broglie wavelength be**

**(b) Also find the de-Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of $\frac{3}{2} k T$ at 300 K.**

**Given $h=6.63 \times 10^{-34} \mathrm{Js}, m_{n}=1.675 \times 10^{-27} \mathrm{kg}$**

**$k=1.38 \times 10^{-23} \mathrm{JK}^{-1}$**[NCERT]

**Q. The work function for the following metals is given $\therefore \quad \mathrm{Na}: 2.75 \mathrm{eV} ; \quad K: 2.30 \mathrm{eV} ; \mathrm{MO}: 4.17 \mathrm{eV} ; \mathrm{Ni}: 5.15 \mathrm{eV}$ Which of these metals will not given photoelectric emission for a radiation of wavelength 3300 Å from a He-Cd laser placed 1 m away from the photocell ? What happens if the laser is brought nearer and placed 50 cm away?**[NCERT]

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Since resolving power (R.P.) is inversely proportional to wave length, therefore R.P. of an electron microscope is about $10^{5}$ times that of an optical microscope. In practice, differences in other (geometrical) factors can change their comparison somewhat.

**Q. In an accelerator experiment on high energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy 10.2 BeV into two $\gamma$ -rays of equal energy. What is the wavelength associated with each $\gamma$ -ray $?\left(1 B e V=10^{9} e V\right)$ ?**[NCERT]

**Q. How can de-Broglie wave hypothesis be verified experimentally**

**or**

**Describe Davission and Germer experiment to establish the wave nature of electrons.**

**Q. The value of ground state energy of hydrogen atom is –13.6 eV**

**(i) What does the negative sign signify ?**

**(ii) How much energy is required to take an electron in this atom from the ground state to the first excited state**

**Q. The energy of an electron in an excited hydrogen atom is –3.4 eV. Calculate the angular momentum of the electron according to Bohr’s theory. Plank’s constant $h=6.6 \times 10^{-34} \mathrm{J} \times \mathrm{sec}$**

**Q. The electron in the hydrogen atom passes from the n=4 energy level to the n=1 level. What is the maximum number of photons that can be emitted? and minimum number?**

**Q. Which state of the triply ionised beryllium $\left(B e^{+++}\right)$ has the same orbital radius as that of the ground state of hydrogen? compare the energies of the two states?**[NCERT]

**Q. 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom transits from the upper level to the lower level**[NCERT]

**Q. Ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state**[NCERT]

**Q. The radius of innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \mathrm{m}$. What are the radii of and orbits ?**[NCERT]

**Q. The ground state energy of hydrogen atom is If an electron makes a transition from an energy level –0.85 eV to –3.4 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum, does this wavelength belong**

**Q. What is the shortest wavelength present in the Paschen series of spectral lines**. [NCERT]

**Q.**The

**total energy of electron in the first excited state of hydrogen atom is about –3.4 eV.**

**(a) What is kinetic energy of electron in this state**

**(b) What is potential energy of electron in this state**

**(c) Which of the answers above would change if the choice of zero of potential energy is changed**[NCERT]

**Q.**From

**the relation $R=R_{0} A^{1 / 3}$ where is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e., independent of A).**[NCERT]

**Q. Draw a graph showing the variation of binding energy per nucleon with mass number of different nuclei. Mark the region where the nuclei are most stable. Give the reason for the decrease of binding per nucleon for nuclei with high mass numbers.**

**Q. Derive the relationship between decay constant $(\lambda)$ and half life time $\left(T_{1 / 2}\right)$ of a radioactive sample**

**Q. Draw a graph showing the variation of potential energy of a pair of nucleons as a function of their separation. Indicate the regions in which nuclear force is (i) Attractive (ii) Repulsive**

**Q. Show that the decay rate ‘R’ of a sample of a radionuclide is related to the number of radioactive nuclei ‘N’ at the same instant by the expression $R=\lambda N$**

**Q. Write nuclear reaction equations for $[\mathrm{NCERTI}]$**

**(i) $\alpha$ decay of $\mathrm{Ra}^{226} \quad$ (iii) $\alpha$ decay of $_{94} P u^{242}$**

**(iii) $\beta^{-}$ decay of $_{15} P^{32} \quad$ (iv) $\beta^{-}$ decay of $_{83} B i^{210}$**

**(v) $\beta^{+}$ decay of $_{6}^{15} C^{11} \quad$ (vi) $\beta^{+}$ decay of $_{43} T c^{97}$**

**(vii) Electron capture of $_{54} X e^{120}$**

**Q. Obtain the approximate value of the radius of (a) a**

**nucleus of $2^{H e^{4}}$ and (b) a nucleus of $g U^{288}(\mathrm{c})$**

**What is the ratio of these radii? Assume**

**$R_{0}=1.2 \times 10^{-15} \mathrm{m}$**[NCERT]

**Q. A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity, assume that the coin is entirely made of $_{29} C u^{63}$ atoms (of mass 62.92960 u). The masses of proton and neutron are 1.00783 u and 1.00867 u respectively**[NCERT]

**Q. A radioactive isotope has a half life of T years. After how much time is its activity reduced to (a) 3.125% (b) 1% of its original activity?**[NCERT]

**Q. The nucleus $_{10} N e^{23}$ decays by $\beta^{-}$ emission. Write down the decay equation and determine the maximum kinetic energy of the electrons emitted from the following data**[NCERT]

**The $B^{-}$ decay of $_{10} N e^{23}$ may be represented as**

**$_{10} N e^{23} \rightarrow_{11} N a^{23}+_{-1} e^{0}+\bar{v}+Q$**Ignoring the rest mass of antineutrino $(\bar{v})$ and electron

**Q. A 1000 MW fission reactor consumes half of its fuel in 5.00 y. How much did it contain initially ? Assume that all the energy generated arises from the fission of and that this nuclide is consumed by the fission process.**[NCERT]

**In the fission of one nucleus of $_{92} U^{285}$ energy**

**generated is 200 $M e V .$**

**Q. How long can an electric lamp of 100 W be kept glowing by fusing of 2.0 kg of deuterium ? The fusion reaction can be taken as**[NCERT]

**Q. Calculate binding energy per nucleon of**

**$40 \mathrm{Ca}$ nucleus (given mass of $\frac{40}{20} \mathrm{Ca}=39.962589 \mathrm{u}$**

**mass of proton $=1.0078254,$ mass of neutron**

**$=1.0086654$ 1 atomic mass unit $(1 \mathrm{u})=931 \mathrm{MeV})$**

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