What is the de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m?

1. $\frac{h}{\sqrt{mkT}}$

2. $\frac{h}{\sqrt{3mkT}}$

3. $\frac{2h}{\sqrt{3mkT}}$ $$

4. $\frac{2h}{\sqrt{mkT}}$

If an electron of mass m with a de-Broglie wavelength of \(\lambda\) falls on the target in an X-ray tube, the cut-off wavelength ( λ₀) of the emitted X-ray will be:

1. ${\lambda }_0=\frac{2mc{\lambda }^2}{h}$         

2. ${\lambda }_0=\frac{2h}{mc}$

3. ${\lambda }_0=\frac{2m^2{c}^2{\lambda }^3}{h^2}$       

4. ${\lambda }_0=\lambda$

Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectron will reach the anode A, if the stopping potential of A relative to C is:

1. +3 V

2. +4 V

3. - 1V

4. -3 V

A certain metallic surface is illuminated with monochromatic light of wavelength λ. The stopping potential for photoelectric current for this light is 3V_o. If the same surface is illuminated with light of wavelength 2λ, the stopping potential is V_o. The photoelectric effect's threshold wavelength for this surface is?

1. 6λ

2. 4λ

3. λ/4

4. λ/6

Which of the following figures represents the variation of the particle momentum and the associated de-Broglie wavelength?

1.		2.
3.		4.

A photoelectric surface is illuminated successively by monochromatic light of wavelengths λ and λ/2. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface of the material will be:
(h = Planck’s constant, c = speed of light)

1. hc/2λ

2. hc/λ

3. 2hc/λ

4. hc/3λ

Light with a wavelength of 500 nm is incident on a metal with a work function of 2.28 eV. The de Broglie wavelength of the emitted electron will be:
1. \( <2.8 \times 10^{-10} \mathrm{~m} \)
2. \( <2.8 \times 10^{-9} \mathrm{~m} \)
3. \( \geq 2.8 \times 10^{-9} \mathrm{~m} \)
4. \( <2.8 \times 10^{-12} \mathrm{~m}\)

When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons emitted from a metal surface increases from 0.5 eV to 0.8 eV. The work function of the metal will be:
1. 0.65 eV

2. 1.0 eV

3. 1.3 eV

4. 1.5 eV

What will be the percentage change in the de-Broglie wavelength of the particle if the kinetic energy of the particle is increased to 16 times its previous value?
1. 25
2. 75
3. 60
4. 50

The wavelength \(\lambda_{e}\) of an electron and \(\lambda_{p}\) of a photon of the same energy E are related as:

1. ${\lambda }_p\propto {{\lambda }_e}^2$

2. ${\lambda }_p\propto {\lambda }_e$ 

3. ${\lambda }_p\propto \sqrt{{\lambda }_e}$

4. ${\lambda }_p\propto \frac{1}{\sqrt{{\lambda }_e}}$