An electron of mass m and a photon have the same energy E. Find the ratio of de-Broglie wavelength associated with the electron to that associated with the photon. (c is the velocity of light)

^{$1.$ ${\left(\frac{E}{2m}\right)}^{1/2}$
$$
$2.$ $c{\left(2mE\right)}^{1/2}$
$$
$3.$ $\frac{1}{c}{\left(\frac{2m}{E}\right)}^{1/2}$
$$
$4.$ $\frac{1}{c}{\left(\frac{E}{2m}\right)}^{1/2}$}
 

A radiation of energy 'E' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (c=velocity of light)

1. E/c

2. 2E/c

3. 2E/c²

4. E/c²

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

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

For photoelectric emission from certain metal, the cut-off 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)

1. $\sqrt{h\nu /\left(2m\right) }$

2. $\sqrt{h\nu /\left(m\right) }$

3. $\sqrt{2h\nu /\left(m\right) }$

4. none of these

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

A 200W sodium street lamp emits yellow light of wavelength $0.6 \mu m.$ Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is 

(1) $1.5\times {10}^{20}$                               

(2) $6\times {10}^{18}$

(3) $62\times {10}^{20}$                                 

(4) $3\times {10}^{19}$