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

1.	\(\frac{h}{\sqrt{m k T}}\)	2.	\(\frac{h}{\sqrt{3 m k T}}\)
3.	\(\frac{2 h}{\sqrt{3 m k T}}\)	4.	\(\frac{2 h}{\sqrt{m k T}}\)

When a metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2$\lambda$, the stopping potential is $\frac{V}{4}$ .The threshold wavelength for metallic surface is:

(a) 5$\lambda$                (b)$\frac{5}{2}$$\lambda$

(c) 3$\lambda$                (d) 4$\lambda$

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)

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

A radiation of energy 'E' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (c=velocity of light)

1. E/c

2. 2E/c

3. 2E/c²

4. E/c²

Which of the following figures represents the variation of the particle momentum and the associated de-Broglie wavelength?

1.		2.
3.		4.

Light with a wavelength of \(500\) nm is incident on a metal with a work function of \(2.28\) eV. The de Broglie wavelength of the emitted electron will be:
1. \( <2.8 \times 10^{-10}~\text{m} \)
2. \( <2.8 \times 10^{-9}~\text{m} \)
3. \( \geq 2.8 \times 10^{-9}~\text{m} \)
4. \( <2.8 \times 10^{-12}~\text{m} \)