A photoelectric surface is illuminated successively by the monochromatic light of wavelength $\lambda$ and $\frac{\lambda}{2}$. 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. $\dfrac{hc}{2\lambda}$

2. $\dfrac{hc}{\lambda}$

3. $\dfrac{2hc}{\lambda}$

4. $\dfrac{hc}{3\lambda}$

Light of wavelength $500~\text{nm}$ is incident on metal with work function $2.28~\text{eV}$. The de-Broglie wavelength of the emitted electron is:

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 $0.5~\text{eV}$ to $0.8~\text{eV}$. The work function of the metal is:
1. $0.65~\text{eV}$
2. $1.0~\text{eV}$
3. $1.3~\text{eV}$
4. $1.5~\text{eV}$

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 $2\nu$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be:
($m$ is the electron mass)