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Dual Nature of Radiation and Matter question

2016 · Q134
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Dual Nature of Radiation and Matter question

2016 · Q134

NEETPhysicsDual Nature of Radiation and MatterMCQ+4 / −1
When a metallic surface is illuminated with radiation of wavelength λ\lambdaλ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2 λ\lambdaλ, the stopping potential is V4{V \over 4}4V​. The threshold wavelength for the metallic surface is
  1. A
    52λ{5 \over 2}\lambda25​λ
  2. B
    3λ\lambdaλ
  3. C
    4λ\lambdaλ
  4. D
    5λ\lambdaλ
View written solutionFree

Correct answer: B

According to Einstein's photoelectric effect,

eV = hcλ{{hc} \over \lambda }λhc​ - hcλ0{{hc} \over {{\lambda _0}}}λ0​hc​ .......(1)

eV4{V \over 4}4V​ = hc2λ{{hc} \over 2\lambda }2λhc​ - hcλ0{{hc} \over {{\lambda _0}}}λ0​hc​ .......(2)

Dividing equation (i) by (ii) by,

4 = 1λ−1λ012λ−1λ0{{{1 \over \lambda } - {1 \over {{\lambda _0}}}} \over {{1 \over {2\lambda }} - {1 \over {{\lambda _0}}}}}2λ1​−λ0​1​λ1​−λ0​1​​

⇒\Rightarrow⇒ λ\lambda λ0 = 3λ\lambda λ

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