Assignment Problems

ASSIGNMENT PROBLEMS 

1. In Compton scattering, the incident photons have a wavelength 0.5 nm. Calculate the wavelength of scattered radiation if they are viewed at angle of 45° to the direction of incidence.

[Ans: λ'=0.5007 nm]

2. X-rays of 1.0 Å are scattered from a carbon block. Find the wavelength of the scattered beam in a direction making 60° with the incident beam. How much kinetic energy is imparted to the recoiling electron? 

[Ans: λ' = 1.0121 Å K.E. = 149 eV]

3. Find the change in the wavelength of an X-ray photon when it is scattered through an angle of 180°. 

[Ans: 0.0484 Å]

4. Monochromatic X-rays of wavelength 0.7078 Å are scattered by carbon at an angle of 90° with the direction of incident beam. What is the wavelength of scattered X-rays?

[Ans: 0.7320 Å ] 

5. Estimate the potential difference through which a proton is needed to be accelerated so that its de Broglie wavelength becomes equal to 1 Å. 

(Given mass of proton = 1.673 x 10-4 kg.) 

[V = 0.082 V]

6. Calculate the de Broglie wavelength associated with an electron carrying an energy 2000 eV. 

[λ = 2.74 × 10-11 m]

7. Prove that the de Broglie wavelength of an electron accelerated through a potential difference of V volts is

8. Calculate the zero point energy for an electron in a one dimensional box of width 10 Å.

[ Ans: 0.376 eV ]

9. A beam of X-rays are scattered by free electrons. At 45° from the beam direction, the At scattered X-rays have a wavelength of 0.022 Å. What is the wavelength of the incident beam?

(Ans: 0.0149 Å) 

10. X-rays, 'of wavelength 0.324 Å are scattered by a carbon block. Find the wavelengh of scattered X-rays for a scattering angle of 180°.

(Ans: 0.1725 Å)

11. X-rays of wavelength 0.3 Å undergoes Compton scattering at an angle of 60°. Find the wavelength of the scattered photon and energy of the recoil electron.

(Ans: λ = 0.3121, E = 2.571 × 10-16 J)

12. Calculate the de Broglie wavelength of an electron accelerated to a potential of 2 kV.

(Ans: 0.2744 Å)