In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of…

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (λ) of incident light and the corresponding stopping potential V0 are given below:
 
λμm V0Volt
0.3 2.0
0.4 1.0
0.5 0.4

Given that c=3×108 ms-1 and e=1.6×10-19C,  Planck's constant (in units of J s) found from such an experiment is :
  1. 6.0×10-34
  2. 6.4×10-34
  3. 6.6×10-34
  4. 6.8×10-34

Solution

KEmax=hCλ-ϕ

eV0=hCλ-ϕ
1.6×10-19×2=h×3×1083000×10-10-ϕ .....(i)
1.6×10-19×1=h×3×1084000×10-10-ϕ .......(ii)
From (ii) ϕ=h×3×1084000×10-10-1.6×10-19

Using value of ϕ in equation (i), we get
1.6×10-19×2=h×3×1083000×10-10-h×3×1084000×10-10+1.6×10-19
1.6×10-19=h×3×10810-713-14=h×3×10810-74-312
1.6×10-19=h×3×10810-7×112
1.6×4×10-19×10-7108=h
6.4×10-34Js=h

Asked in: JEE Advanced 2016 (Paper 1)

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