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. \(\lambda_0\)

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. $\frac{2h}{\sqrt{mkT}}$

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. ${\lambda }_0=\lambda$

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)

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