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Q.

If a surface has a work function 4.0 eV, what is the maximum velocity of electrons liberated from the surface when it is irradiated with ultraviolet radiation of wavelength $0.2 μm$ ?

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a

$4 .4 \times 10^{7} {ms}^{- 1}$

b

$4 .4 \times 10^{5} {ms}^{- 1}$

c

$8 .8 \times 10^{7} {ms}^{- 1}$

d

$8 .8 \times 10^{5} {ms}^{- 1}$

answer is C.

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Detailed Solution

Energy of the incident radiation

$\begin{array}{l} E = \frac{12375}{0.2 \times 10^{4}} = 6 .19 eV \\ \frac{1}{2} {mv}_{max}^{2} = E - ϕ = (6 .19 - 4) eV = 2.19 eV \\ or v_{max}^{} = \sqrt{\frac{2 \times 2 .19 \times 1 .6 \times 10^{- 19}}{9.11 \times 10^{- 31}}} \\ or v_{max}^{} \approx 8.8 \times 10^{5} {ms}^{- 1} \end{array}$

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If a surface has a work function 4.0 eV, what is the maximum velocity of electrons liberated from the surface when it is irradiated with ultraviolet radiation of wavelength 0.2 μm?