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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, it is found to liberate electrons with kinetic energies E1 and E2 respectively. The value of Planck's constant can be found from which of the relation

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

The correct option is D h=(E1E2)λ1λ2c(λ2λ1)
If W0 is the ionization energy of hydrogen atom, the incident energy first ionizes the atom and rest of the energy is given in the kinetic energy.
hcλ1=W0+E1
hcλ2=W0+E2
Subtracting the two equations gives,
h=(E1E2)λ1λ2c(λ2λ1)
So, the answer is option (C).

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