A photoelectric surface is illuminated successively by the monochromatic light of wavelength $\mathrm{\lambda }$ and $\frac{\mathrm{\lambda }}{2}$. 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 mineral is:
[h=Plank’s constant, c=speed of light]

1. $\frac{hc}{2\lambda }$

2. $\frac{hc}{\lambda }$

3. $\frac{2hc}{\lambda }$

4. $\frac{hc}{3\lambda }$

Light of wavelength 500 nm is incident on metal with work function 2.28 eV. The de-Broglie wavelength of the emitted electron is:

1. \(< 2.8\times 10^{-10}\) m

2. \(< 2.8\times 10^{-9}\) m

3. \(\geq 2.8\times 10^{-9}\) m

4. \(\leq 2.8\times 10^{-12}\) m

Radiation of energy 'E' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:
(c = velocity of light)
1. \(E \over c\)
2. \(2E \over c\)
3. \(2E \over c^2\) 
4. \(E \over c^2\)

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

1.		2.
3.		4.

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 is:

1. 0.65 eV

2. 1.0 eV

3. 1.3 eV

4. 1.5 eV

If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is:

1. 25

2. 75

3. 60

4. 50

For photoelectric emission from certain metals, the cutoff frequency is $\nu$. If radiation of frequency 2$\mathrm{\nu }$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be:
(m is the electron mass)

1. $\sqrt{\mathrm{h\nu }/\mathrm{m}}$

2. $\sqrt{2\mathrm{h\nu }/\mathrm{m}}$

3. $2\sqrt{\mathrm{h\nu }/\mathrm{m}}$

4. $\sqrt{\mathrm{h\nu }/\left(2\mathrm{m}\right)}$