SATHEE: Dual Nature of Radiation and Matter

Dual Nature of Radiation and Matter - Result Question 26

28. A photoelectric surface is illuminated successively by monochromatic light of wavelength $λ$ and $\frac{λ}{2}$ . If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface of the material is : ( $h =$ Planck’s constant, $c =$ speed of light $)$

[2015 RS]

(a) $\frac{h c}{λ}$

(b) $\frac{2 h c}{λ}$

(d) $\frac{h c}{2 λ}$

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Answer:

Correct Answer: 28. (d)

Solution:

(d) Photoelectric equations

$E k_{1 max} = \frac{h c}{λ} - ϕ$

and $E k_{2 max} = \frac{h c}{λ / 2} - ϕ$

$E K_{2 max} = \frac{2 h c}{λ} - ϕ$ From question, $E k_{2 max} = 3 E k_{1 max}$

Multiplying equation (i) by 3

$3 E k_{1 max} = 3 (\frac{h c}{λ} - ϕ)$

From equation (ii) and (iii)

$\frac{3 h c}{λ} - 3 ϕ = \frac{2 h c}{λ} - ϕ ∴ ϕ ($ work function $) = \frac{h c}{2 λ}$

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Dual Nature of Radiation and Matter - Result Question 26

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