# Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited state to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the materials is: Option 1) $4\times 10^{15}\: \: Hz$ Option 2) $5\times 10^{15}\: \: Hz$ Option 3) $1.6\times 10^{15}\: \: Hz$ Option 4) $2.5 \times 10^{15}\: \: Hz$

As we learnt in

Conservation of energy -

$h\nu = \phi _{0}+\frac{1}{2}mv^{2}_{max}$

$h\nu = h\nu _{0}+\frac{1}{2}mv^{2}_{max}$

$h\left ( \nu-\nu _{0} \right )=\frac{1}{2}mv^{2}_{max}$

$where, h - Plank's constant\ \nu - Frequency\ \nu_{0} - threshold\ frequency\ \phi_{0}- work function$

- wherein

Amount of energy radiated when electron jump from n = 2 to n = 1

$\Delta E=13.6\:(1-\frac{1}{4})\:=\:10.2\:eV$

Then  $eV_{s}\:=\:\frac{hc}{\lambda }-\phi$

$\phi = 10.2\:eV-3.57\:eV$

$= 6.63\:eV\:=\:h\upsilon$

Threshold frequency = $\frac{6.63\times1.6\times10^{-19}}{6.62\times10^{-34}}$$=\:1.6\times10^{15}\:HZ$

Option 1)

$4\times 10^{15}\: \: Hz$

Incorrect

Option 2)

$5\times 10^{15}\: \: Hz$

Incorrect

Option 3)

$1.6\times 10^{15}\: \: Hz$

Correct

Option 4)

$2.5 \times 10^{15}\: \: Hz$

Incorrect

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