When monochromatic light of wavelength $\mathrm{\lambda }$ illuminates a metal surface then stopping potential for photoelectric current is 3${\mathrm{V}}_0$. If wavelength changes to 2$\mathrm{\lambda }$ then stopping potential becomes $V_0$. Stopping potential in case wavelength is changed to 3$\mathrm{\lambda }$, would be:

1.  $\frac{{\mathrm{V}}_0}{2}$

2.  $\frac{{\mathrm{V}}_0}{6}$

3.  $\frac{{\mathrm{V}}_0}{4}$

4.  $\frac{{\mathrm{V}}_0}{3}$

The stopping potential for photoelectrons emitted from a surface illuminated by the light of wavelength 400 nm is 500 mV. When the incident wavelength is changed to a new value, the stopping potential is found to be 800 mV. New wavelength is about:

1.  365 nm

2.  250 nm

3.  640 nm

4.  340 nm

Assume that sodium produces monochromatic light of wavelength $5.89 x {10}^{-7}$ m. At what approximate rate would a 10-watt sodium-vapor light be emitting photons? Assume that the efficiency of the light bulb is about 30%.

1.  8.9 x ${10}^{18}$ photons/s

2.  3.0 x ${10}^{19}$ photons/s

3.  9.9 x ${10}^{19}$ photons/s 

4.  2.0 x ${10}^{20}$ photons/s

In a photoelectric experiment, it was found that the stopping potential decreases from 2.5 V to V as the wavelength of the light is varied from 3$\mathrm{\lambda }$ to 4$\mathrm{\lambda }$. Calculate the Planck's constant in terms of V, $\mathrm{\lambda }$ and speed of light (c).

1.  $\frac{9\mathrm{\lambda eV}}{\mathrm{c}}$

2.  $\frac{6\mathrm{\lambda eV}}{\mathrm{c}}$

3.  $\frac{9\mathrm{\lambda eV}}{4\mathrm{c}}$

4.  $\frac{18\mathrm{\lambda eV}}{\mathrm{c}}$

The photoelectric effect is observed for two frequencies of 3 x ${10}^{14}$ Hz and 2 x ${10}^{14}$ Hz of incident radiation. If maximum kinetic energies are in ratio 2:1, then threshold frequency is
 

1.  ${10}^{14}$ Hz

2.  $\frac{3}{2} \times {10}^{14} \mathrm{Hz}$

3.  $\frac{4}{3}\times {10}^{14} \mathrm{Hz}$

4.  None of these

An electron is in an excited state in a hydrogen-like atom. It has a total energy of -3.4 eV. The kinetic energy of the electron is E and its de-Broglie wavelength is $\lambda$. Then:

1.  E = 6.8 eV, $\mathrm{\lambda }$ = 6.6 x ${10}^{-10}$ m

2.  E = 3.4 eV, $\mathrm{\lambda }$ = 6.6 x ${10}^{-10}$ m

3.  E = 6.6 eV, $\mathrm{\lambda }$ = 6.6 x ${10}^{-11}$ m

4.  E = 6.8 eV, $\mathrm{\lambda }$ = 6.6 x ${10}^{-11}$ m

Radiation of wavelength $\frac{{\mathrm{\lambda }}_0}{3}$ (${\mathrm{\lambda }}_0$ being the threshold wavelength) is incident on a photosensitive sphere of radius R. The charge developed on the sphere when electrons cease to be emitted will be-

1.  $\frac{4{\mathrm{\pi \epsilon }}_0\mathrm{Rhc}}{{\mathrm{e\lambda }}_0}$

2.  $\frac{6{\mathrm{\pi \epsilon }}_0\mathrm{Rhc}}{{\mathrm{e\lambda }}_0}$

3.  $\frac{8{\mathrm{\pi \epsilon }}_0\mathrm{Rhc}}{{\mathrm{e\lambda }}_0}$

4.  $\frac{12{\mathrm{\pi \epsilon }}_0\mathrm{Rhc}}{{\mathrm{e\lambda }}_0}$

In an experiment on the photoelectric effect. the wavelength of the incident radiation is $\lambda$. The wavelength of the incident radiation is reduced to $\frac{1}{3}$rd of the initial value and the maximum kinetic energy of the photoelectron is observed to be n times the previous value. The threshold wavelength for the metal plate is :

1.  $\left(\frac{\mathrm{n} - 1}{\mathrm{n} - 3}\right)\mathrm{\lambda }$

2.  $\left(\frac{\mathrm{n}}{\mathrm{n} - 3}\right)\mathrm{\lambda }$

3.  $\frac{\left(\mathrm{n} + 1\right)\mathrm{\lambda }}{\left(\mathrm{n} - 3\right)}$

4.  $\frac{\mathrm{\lambda }}{\mathrm{n}}$

According to the Bohr model of the atom, an electron undergoes a transition from one orbit that is closer to the nucleus to another which is farther from the nucleus by absorbing a photon whose energy E depends on its frequency f as E = hf, where h is Planck's constant. The energy of 13.6 eV is needed to ionize a hydrogen atom by ejecting an electron from the lowest energy level. What is the longest wavelength of a photon that can eject the electron from the lowest energy level of the atom?

1.  40 nm

2.  60 nm

3.  80 nm

4.  90 nm

Photons of energy 7 eV are incident on two metals A and B with work functions 6 eV and 3 eV respectively. The minimum de-Broglie wavelengths of the emitted photoelectrons with maximum energies are ${\lambda }_A$ and ${\lambda }_B$, respectively where $\frac{{\lambda }_A}{{\lambda }_B}$ is nearly-

1.  0.5

2.  1.4

3.  4.0

4.  2.0