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Question

Ultraviolet light of wavelength λ1 and λ2(λ2>λ1)when allowed to fall on hydrogen atoms in their ground state is found to liberate electrons with kinetic energies E1and E2 respectively. The value of Planck's constant can be found from the relation :
  1. h=1c(λ2λ1)(E1E2)
  2. h=(E1+E2)λ1λ2c(λ2+λ1)
  3. h=(E1E2)λ1λ2c(λ2λ1)
  4. h=1c(λ2+λ1)(E1+E2)

A
h=(E1E2)λ1λ2c(λ2λ1)
B
h=(E1+E2)λ1λ2c(λ2+λ1)
C
h=1c(λ2λ1)(E1E2)
D
h=1c(λ2+λ1)(E1+E2)
Solution
Verified by Toppr

Suppose the frequency of the photons are ν1 and ν2 (ν1>ν1). Where, ν=c/λ.
According to the question:
hν1E0=E1
hν2E0=E2 , where, E0 is the ionization energy of the hydrogen.
Solving this two equation we will get:

h=(E1E2)λ1λ2c(λ2λ1).

So, the answer is option (C).

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