In case of photoelectric emission from certain metal, the cutoff frequency is ν . If the radiation of frequency 3 ν is incident on the metal plate, the maximum possible velocity of the emitted electro

Question

In case of photoelectric emission from certain metal, the cutoff frequency is ν . If the radiation of frequency 3 ν is incident on the metal plate, the maximum possible velocity of the emitted electrons will be ( m = mass of electron, h = Planck's constant)

TestHub · Accepted Answer

According to Einstein's photoelectric equation:

$K_{max} = h ν_{incident} - h ν_{cutoff}$

Given $ν_{incident} = 3 ν$ and $ν_{cutoff} = ν$ :

$\frac{1}{2} m v_{max}^{2} = h (3 ν) - h ν$

$\frac{1}{2} m v_{max}^{2} = 2 h ν$

$v_{max}^{2} = \frac{4 h ν}{m}$

$v_{max} = 2 \frac{h ν}{m}$

Answer: $2 (\frac{h ν}{m})$

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