An electron of mass m with an initial velocity $\overrightarrow{v}={\mathrm{v}}_0\hat{i}$ \( ( v_o > 0 ) \) enters in an electric field $\overrightarrow{\mathrm{E}}=-E_0\hat{i}$ (E_o = constant >0) at t = 0. If ${\mathrm{\lambda }}_0$, is its de-Broglie wavelength initially, then what will be its de-Broglie wavelength at time t?

1. $\frac{{\mathrm{\lambda }}_0}{\left(1+{\displaystyle \frac{{\mathrm{eE}}_0}{{\mathrm{mv}}_0}}\mathrm{t}\right)}$

2. ${\mathrm{\lambda }}_0\left(1+\frac{{\mathrm{eE}}_0}{{\mathrm{mv}}_0}\mathrm{t}\right)$

3. ${\mathrm{\lambda }}_0\mathrm{t}$

4. ${\mathrm{\lambda }}_0$

When the light of frequency \(2\nu_0\) (where \(\nu_0\) is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v₁. When the frequency of the incident radiation is  increased to \(5\nu_0,\) the maximum velocity of electrons emitted from the same plate is v₂. What will be the ratio of v₁ to v₂?
1. 1 : 2
2. 1 : 4
3. 4 : 1
4. 2 : 1

What is the de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m?

1. $\frac{h}{\sqrt{mkT}}$

2. $\frac{h}{\sqrt{3mkT}}$

3. $\frac{2h}{\sqrt{3mkT}}$ $$

4. $\frac{2h}{\sqrt{mkT}}$

The photoelectric threshold wavelength of silver is 3250 x 10^-10 m. What will be the velocity of the electron ejected from a silver surface by the ultraviolet light of wavelength 2536 x 10^-10 m?

(Given h= $4.14\times {10}^{-15}$ $\mathrm{eVs}$ and $\mathrm{c}=3\times {10}^8$ ${\mathrm{ms}}^{-1}$)

1. $\approx 0.6\times {10}^6$ ms^-1
2. $\approx 61\times {10}^3$ ms^-1
3. $\approx 0.3\times {10}^6$ ms^-1
4. \(\approx 0.3\times 10^5\) ms^-1

If an electron of mass m with a de-Broglie wavelength of \(\lambda\) falls on the target in an X-ray tube, the cut-off wavelength ( λ₀) of the emitted X-ray will be:

1. ${\lambda }_0=\frac{2mc{\lambda }^2}{h}$         

2. ${\lambda }_0=\frac{2h}{mc}$

3. ${\lambda }_0=\frac{2m^2{c}^2{\lambda }^3}{h^2}$       

4. ${\lambda }_0=\lambda$

Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectron will reach the anode A, if the stopping potential of A relative to C is:

1. +3 V

2. +4 V

3. - 1V

4. -3 V

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)

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