Dual Nature of Radiation and Matter - Result Question 25

27. Light of wavelength $500 n m$ is incident on a metal with work function $2.28 e V$ . The wavelength of the emitted electron is:

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======= ####27. Light of wavelength $500 n m$ is incident on a metal with work function $2.28 e V$ . The wavelength of the emitted electron is:

c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (a) $< 2.8 \times 10^{- 9} m$

(b) $\geq .2 .8 \times 10^{- 9} m$

(c) $\leq 2.8 \times 10^{- 12} m$

(d) $< 2.8 \times 10^{- 10} m$

[2015 RS]

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Answer:

Correct Answer: 27. (b)

Solution:

(b) Given : Work function $ϕ$ of metal $= 2.28 e V$ Wavelength of light $λ = 500 n m = 500 \times 10^{- 9} m$

$K E_{max} = \frac{h c}{λ} - ϕ$

$K E_{max} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{5 \times 10^{- 7} \times 1.6 \times 10^{- 19}} - 2.28$

$K E_{max} = 2.48 - 2.28 = 0.2 e v$

$λ_{min} = \frac{h}{p} = \frac{h}{\sqrt{2 m (K E)_{max}}}$

$= \frac{\frac{20}{3} \times 10^{- 34}}{\sqrt{2 \times 9 \times 10^{- 31} \times 0.2 \times 1.6 \times 10^{- 19}}}$

$λ_{min} = \frac{25}{9} \times 10^{- 9}$

$= 2.80 \times 10^{- 9} n m ∴ λ \geq 2.8 \times 10^{- 9} m$

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