Light of wavelength \(500~\text{nm}\) is incident on metal with work function \(2.28~\text{eV}\). The de-Broglie wavelength of the emitted electron is:

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

1.		2.
3.		4.

If the kinetic energy of the particle is increased to \(16\) times its previous value, the percentage change in the de-Broglie wavelength of the particle is:
1. \(25\)
2. \(75\)
3. \(60\)
4. \(50\)

An \(\alpha\text-\)particle moves in a circular path of radius \(0.83~\text{cm}\) in the presence of a magnetic field of \(0.25~\text{Wb/m}^2\). The de-Broglie wavelength associated with the particle will be:
1. \(1~\mathring{\text{A}}\)
2. \(0.1~\mathring{\text{A}}\)
3. \(10~\mathring{\text{A}}\)
4. \(0.01~\mathring{\text{A}}\)

If the momentum of an electron is changed by \(P,\) then the de-Broglie wavelength associated with it changes by \(0.5\%.\) The initial momentum of an electron will be:
1. \(400P\)
2. \(\frac{P}{100}\)
3. \(100P\)
4. \(200P\)

A radioactive nucleus of mass M emits a photon of frequency $\nu$ and the nucleus will recoil. The recoil energy will be:

1.  $\frac{{\mathrm{h}}^2{\mathrm{\nu }}^2}{2{\mathrm{Mc}}^2}$

2.  zero

3.  $\frac{\mathrm{h\nu }}{\mathrm{c}\sqrt{2\mathrm{M}}}$

4.  $\frac{\mathrm{c}\sqrt{2\mathrm{M}}}{\mathrm{h\nu }}$

A particle of mass \(1\) mg has the same wavelength as an electron moving with a velocity of  \(3\times 10^{6}\) ms^-1. The velocity of the particle is:
(Mass of electron = \(9.1 \times 10^{-31}\) kg)
1. \(2.7 \times 10^{-18}~\text{ms}^{-1}\)
2. \(9 \times 10^{-2}~\text{ms}^{-1}\)
3. \(3 \times 10^{-31}~\text{ms}^{-1}\)
4. \(2.7 \times 10^{-21}~\text{ms}^{-1}\)