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Q.

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

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a

0.61 eV

b

0.81 eV

c

0.52 eV

d

1.02 eV

answer is A.

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Detailed Solution

$\begin{array}{l} KE = h v - ϕ \\ Initial incident energy = h v_{1} = \frac{12420}{5000} = 2.484 e V \\ F i n al incident energy = h v_{2} = \frac{12420}{2000} = 6.21 e V \\ I n i t i a l K i n e t i c e n e r g y = K = 2.484 - ϕ \\ F i n a l K i n e t i c e n e r g y = 3 K = 6.21 - ϕ \\ D i v i d i n g w e g e t, \\ \Rightarrow \frac{1}{3} = \frac{2.484 - ϕ}{6.21 - ϕ} \\ \Rightarrow ϕ = 0.621 e V \end{array}$

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When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :