CBSE Class 12 Physics Modern Physics Advanced Problems

CBSE Class 12 Physics Modern Physics Advanced Problems. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

1. A mu-meson, of chage –e and mass 207 times that of an electron, can be captured by a proton to form a hydrogen like “mesic atom”. Calculate the radius of the first Bohr orbit, the binding energy and the wavelength of the first line in the Lyman series for such an atom. The mass of the proton is 1836 times the mass of an electron. The radius of the first Bohr orbit and the binding energy of hydrogen are 0.53 Å and 13.6 eV respectively.

2. A monochromatic light source of frequency v illuminates a metallic surface and ejects photoelectrons. The photoelectrons having maximum energy are just able to ionize the hydrogen atom in the ground state. When this experiment is repeated with an incident radiation of frequency 5v/6 , the photoelectrons so emitted are able to excite the hydrogen atom beam which then emit a radiation of wavelength 1215 Å. Find the frequency v and work function of the metal.

3. A monochromatic light beam of wavelength 1800 Å ejects wavelength from a plate of a metal whose work function is 2 eV. If a uniform magnetic field of 2 × 10^–5 tesla is applied parallel to the plate, find the radius of the path followed by electrons ejected normally from the plate with maximum energy.

4. Electrons in hydrogen like atoms of atomic number 3 make transitions from the fifth to the fourth orbit and from the fourth to the third orbit. The resulting radiations are incident normally on a metal plate and eject photoelectrons. The stopping potential for the photoelectrons ejected by the shorter wavelength is 3.95 volts. Calculate the work function of the metal and stopping potential for the photoelectrons ejected by longer wavelength.

5. In a chemical analysis of a rock, the mass ratio of two radioactive isotopes is found to be 100 : 1. The mean lives of the two isotopes are 4 × 10⁹ years and 2 × 10⁹ years respectively. It is given that at the time of formation, the atoms of both the isotopes were in equal proportion. Calculate the age of the rock. It is given that the ratio of the atomic weights of two isotopes is 1.02 : 1.

6. Polonium (₈₄Po²¹⁰) emits ₂He⁴ particles and is converted into lead (₈₂Pb²⁰⁶). This reaction is used for producing electric power in a space mission. Po²¹⁰ has a half life of 138.6 days. Assuming an efficiency of 10% for the thermoelectric generator, how much Po²¹⁰ is required to produce 1.2 × 10⁷ J of electric energy per day at the end of 693 days. Also find the initial activity of ₈₄Po²¹⁰. Given that masses of nuclei Po²¹⁰, Pb²⁰⁶ and He⁴ are 209.98264 units, 205.97440 units and 4.00260 units respectively.

7. A stream of mono-energetic neutrons is moving with a kinetic energy of 3.27 × 10^–2 eV. Find the percentage of neutrons which will decay before they travel a distance of 10 m. Given that half life time of neutrons is 700 seconds and mass of neutron is 1.675 × 10^–27 Kg.

8. A deuterium reaction takes place in a fusion reaction in the following two stages :
(a) Two deuterium ₁D² nuclei fuse together to form a tritium nucleus as ₁D² + ₁D² → ₁T³ + E₁.
(b) A tritium nucleus fuses with another deuterium nucleus to produce a helium nucleus and a neutron as ₁T³ + ₁D² → ₂He⁴ + 0n₁ + E₂.
(i) Find the energy E₁ and E₂ released in each of these two stages.
(ii) Find the energy released per deuterium atom in the combined reaction. Given that masses of ₁D², ₁T³, ₂He⁴, ₁H¹ and 0n¹ are 2.014102, 3.016049, 4.002603, 1.007825 and 1.008665 atomic mass units respectively.

9. A nuclear reactor of 200 MW rating used the following nuclear fusion reaction : ₁H² + ₁H² → ₂He⁴ + Q. If the energy Q from this reaction is used with a 25% efficiency in the reaction, find the mass of deuterium fuel which will be required per day. The masses of ₁H² and ₂He⁴ are 2.0141 a.m.u. and 4.0026 a.m.u. respectively.

10. The ionization energy of a hydrogen like atom is 4 Rydberg.

(i) What is the wavelength of radiation emitted when the electron jumps from first excited state to the ground state?
(ii) What is the radius of first orbit for this atom?
Given: Bohr radius of hydrogen atom = 5 × 10^–11 m and 1 Rydberg = 2.2 × 10^–18 J.

11. An energy of 68.0 eV is required to excite a hydrogen like atom from its second Bohr orbit to the third. The nuclear charge is Ze. Find the value of Z, the kinetic energy of the electron in the first Bohr orbit an the wavelength of the radiation required to eject the electron from the first Bohr orbit to infinity.

12. An electron in the ground state of hydrogen atom is revolving in anticlock-wise direction in a circular orbit of radius r.
(i) Obtain an expression for the orbital magnetic dipole moment of the electron.
(ii) The atom is placed in a uniform magnetic induction B such that the plane-normal of the electronorbit makes an angle of 30° with the magnetic induction. Find the torque experienced by the orbiting electron.

13. A moving hydrogen atom makes a head on inelastic collision with a stationary hydrogen atom. Before collision both atoms are in the ground state and after collision they move together. What is the minimum velocity of the moving hydrogen atom if one of the atoms is to be given the minimum excitation energy after the collision.

14. Calculate the wavelength of the emitted characteristic X-ray from a tungsten (Z = 74) target when an electron drops from an M-shell to a vacancy in the K-shell.

15. A potential difference of 20 kV is applied across an X-ray tube. Find the minimum wavelength of X-rays generated.

Advanced Problems
1. 2.84 × 10–3 Å,     2.53 KeV, 6.52 Å 2. 5 × 1015 Hz, 6.875 eV   3. 0.37 m    4. 2.0 eV, 0.75 V   5. 1.834 × 1010 years  6. 10 gm, 4.57 × 1021 per day  7. 4.8 × 10–3 %    8. (a) 4.033 MeV, 17.585 MeV; (b) 7.206 MeV    9. 120 gm  10. 3 × 10–8 m, 2.5 × 10–11 m  11. 6, –489.6 eV, 25.28 Å  12. (i) 2 1evr nˆ ; (ii) me4h B   13. 6.246 × 104 m/sec. 14. 0.0188 × 10–9 m  15. 0.62 Å