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

A 160 watt light source is radiating light of wavelength 6200 Å uniformly in all directions. The photon flux at a distance of 1.8 m is of the order of (Planck's constant $6.63 \mathrm{x} {10}^{-34} \mathrm{J}-\mathrm{s}$) :

1. ${10}^2$  ${\mathrm{s}}^{-1}$

2. ${10}^{12}$  ${\mathrm{s}}^{-1}$

3. ${10}^{19}$  ${\mathrm{s}}^{-1}$

4. ${10}^{25}$  ${\mathrm{s}}^{-1}$

An electron in an electron microscope with initial velocity ${\mathrm{V}}_0\hat{i}$ enters a region of a strong transverse electric field ${\mathrm{E}}_0\hat{\mathrm{j}}$. The time taken for the change in its de-Broglie wavelength from the initial value of $\mathrm{\lambda }$ to $\mathrm{\lambda }/3$ is proportional to :

1.  ${\mathrm{E}}_0$

2.  $\frac{1}{{\mathrm{E}}_0}$

3.  $\frac{1}{\sqrt{{\mathrm{E}}_0}}$

4.  $\sqrt{{\mathrm{E}}_0}$

In the case of the photoelectric effect -

1. Since photons are absorbed as a single unit, there is no significant time delay in the emission of photoelectrons.

2. Einstein's analysis gives a critical frequency ${\nu }_0 = \frac{e\varphi }{h}$, where $\varphi$ is the work function and the light of this frequency ejects electrons with maximum kinetic energy.

3. Only a small fraction of the incident photons succeed in ejecting photoelectrons while most of them are absorbed by the system as a whole and generate thermal energy.

4. The maximum kinetic energy of the electrons is dependent on the intensity of radiation.

In the photoelectric effect, which photons of light dislodge electrons with the highest kinetic energy?

1.  photons of dim blue light

2.  photons of bright red light

3.  photons of very dim violet light 

4.  photons of very bright green light

The threshold frequency of sodium for the photoelectric effect corresponds to yellow light. What happens when the bright yellow light is shone on the sodium metal?

1.  No electrons are released from the metal.

2.  The kinetic energy of the electrons increases.

3.  The number of electrons ejected increases.

4.  The threshold frequency of sodium metal increases.

If the work function of a metal is $6.622 \times {10}^{-20} J$ and a ray of electromagnetic radiation with a frequency of $1.0 \times {10}^{14} Hz$ is incident on the metal, what will be the speed of the electrons ejected from the metal?$( Note:h = 6.626 \times {10}^{-34} J-s \mathrm{and} m_e -=9.1 \times {10}^{-31} kg)$

1.  $2.62 \times {10}^{-6} \frac{m}{s}$

2.  $1.07 \times {10}^{-4} \frac{m}{s}$

3.  $9.38 \times {10}^3 \frac{m}{s}$

4.  $3.81 \times {10}^5 \frac{m}{s}$