An electron of mass m with an initial velocity \(\vec v= v_0\hat i\)$\stackrel{}{}$\( ( v_o > 0 ) \) enters in an electric field\(\vec E = -E_0 \hat i (E_0 = \text{constant}>0)\) at \(t=0\). If \(\lambda_0\)${\mathrm{}}_{}$\(\lambda_0\), is its de-Broglie wavelength initially, then what will be its de-Broglie wavelength at time \(t\)?
1. \(\frac{\lambda_0}{\left(1+ \frac{eE_0}{mv_0}t\right)}\)
2. \(\lambda_0\left(1+ \frac{eE_0}{mv_0}t\right)\)
3. \(\lambda_0 t\)
4. \(\lambda_0\)

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 \(v_1\). When the frequency of the incident radiation is  increased to \(5\nu_0,\) the maximum velocity of electrons emitted from the same plate is \(v_2.\) What will be the ratio of \(v_1\) to \(v_2\)?

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 \(3250\times 10^{-10}~\text{m}\). What will be the velocity of the electron ejected from a silver surface by the ultraviolet light of wavelength \(2536\times 10^{-10}~\text{m}\)? (Given \(h= 4.14\times 10^{-15}~\text{eVs}\)$$ and $\mathrm{}$\(c= 3\times 10^{8}~\text{m/s}\)${\mathrm{}}^{}$)
1. \(\approx 0.6\times 10^{6}~\text{m/s}\)
2. \(\approx 61\times 10^{3}~\text{m/s}\)
3. \(\approx 0.3\times 10^{6}~\text{m/s}\)
4. \(\approx 0.3\times 10^{5}~\text{m/s}\)

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)

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