For certain metal, incident frequency ν is five times threshold frequency ν 0 and the maximum velocity of the photoelectrons is 8 × 10 6 m s - 1 . If ν = 2 ν 0 , the maximum velocity of photoelectrons

Question

For certain metal, incident frequency ν is five times threshold frequency ν 0 and the maximum velocity of the photoelectrons is 8 × 10 6 m s - 1 . If ν = 2 ν 0 , the maximum velocity of photoelectrons will be

TestHub · Accepted Answer

According to Einstein's photoelectric equation

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

$or \frac{1}{2} {mv}_{max}^{2} = h v - h v_{0}$

According to the given problem

$\frac{1}{2} m {(8 \times 1 0^{6})}^{2} = h (5 v_{0} - v_{0}) \dots (i)$

$\frac{1}{2} m v_{max}^{2} = h (2 v_{0} - v_{0}) \dots (i i)$

Dividing equation $(i)$ by $(ii)$

$\frac{{(8 \times 1 0^{6})}^{2}}{v_{max}^{2}} = \frac{4 v_{0}}{v_{0}}$

$v_{max}^{2} = \frac{{(8 \times 1 0^{6})}^{2}}{4}$

$v_{max} = \frac{8 \times 10^{6}}{2} = 4 \times 10^{6} m \sec^{- 1}$

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