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

For photoelectric emission from certain metals, the cutoff frequency is $\nu$. If radiation of frequency 2$\mathrm{\nu }$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be:
(m is the electron mass)

1. $\sqrt{\mathrm{h\nu }/\mathrm{m}}$

2. $\sqrt{2\mathrm{h\nu }/\mathrm{m}}$

3. $2\sqrt{\mathrm{h\nu }/\mathrm{m}}$

4. $\sqrt{\mathrm{h\nu }/\left(2\mathrm{m}\right)}$

A 200 W sodium street lamp emits yellow light of wavelength 0.6 $\mathrm{\mu m}$. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is:

1. $1.5\times {10}^{20}$

2. $6\times {10}^{18}$

3. $62\times {10}^{20}$

4. $3\times {10}^{19}$

An $\mathrm{\alpha }$-particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of 0.25 Wb/m². The de-Broglie wavelength associated with the particle will be:

$1.\; 1 \stackrel{\mathrm{o}}{\mathrm{A}}$

$2.$ $0.1$ $\stackrel{\mathrm{o}}{\mathrm{A}}$

$3.$ $10$ $\stackrel{\mathrm{o}}{\mathrm{A}}$

$4.$ $0.01$ $\stackrel{\mathrm{o}}{\mathrm{A}}$

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 source S₁ is producing 10¹⁵ photons per sec of wavelength 5000 Å. Another source S₂ is producing 1.02×10¹⁵ photons per second of wavelength 5100 Å. Then, (power of S₂)/(power of S₁) is equal to:

1. 1.00

2. 1.02

3. 1.04

4. 0.98