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Question

Light of wavelength λ strikes a photoelectric surface and electrons are ejected with kinetic energy K. If K is to be increased to exactly twice its original value, the wavelength must be changed is λ such that:
  1. λ<λ/2
  2. λ>λ/2
  3. λ>λ>λ/2
  4. λ=λ/2

A
λ<λ/2
B
λ>λ/2
C
λ>λ>λ/2
D
λ=λ/2
Solution
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K=hcλϕ

where ϕ is the work potential.

ϕ=hcλK

Now to increase K to 2K

2K=2hcλ2ϕ

Replacing ϕ

2K=2hcλ2hcλ+2K

λ=λλ+1

Thus, λ<λ. Hence option C is correct.

Also since we are talking about particle nature of light, λ is small,

thus λ>λ2.

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