Question

The ground state energy of hydrogen atom is -13.6eV. The photon emitted during the transition of electron from n = 2 to n = 1 state, is incident on the photosensitive material of unknown work function. The photoelectrons are emitted from materials with a maximum kinetic energy of 8 ev. Calculate the threshold wavelength of the material used.

Answer 1

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Answer 2

The threshold wavelength of the material = 5.625 × (10)^-7 m

The photoelectron makes a transition from n = 2 to n = 1.

Energy released during the transition -

Energy = 13.6 × Z² (1/(n2)² - 1/(n1)²)

Z = 1 for hydrogen atom

n1 = 2 , n2 = 1

Energy = 13.6 × 1 × ( 1 - 1/4 )

= 13.6 × 3/4

= 10.2 eV

The maximum kinetic energy of the photoelectrons = 8 eV

Using Eienstien's photoelectric Equation -

KE (max) = Energy released - W

W is the work function = 10.2 eV

W = 10.2 - 8

W = 2.2 eV

W = hc/λ

c is the velocity of light and λ is the threshold wavelength .

=> 2.2 × 1.6 × (10)^-19 = ( 3 × (10)^8 × 6.6 × (10)^-34)/λ

=> λ = 5.625 × (10)^-7 m

The threshold wavelength of the material = 5.625 × (10)^-7 m