A light source of wavelength λ illuminates a metal and ejects photoelectrons with a maximum kinetic...

A light source of wavelength λ illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1.12 eV. A second light source of wavelength λ/2 ejects photoelectrons with a maximum kinetic energy of 3.60 eV. What is the work function of the metal?

____ eV

Expert Solution

Photo electric equation hf = ϕ + E_k

Frequency , f= c/λ where c is speed of light

λ is wavelength of light.

Φ – work function

E_K –max kinetic energy of photo electrons.

When wavelength of light is λ, hc/λ =ϕ + 1.12 (1) [E_k(λ)=1.12eV]

When wavelength is λ/2, hc/(λ/2) = ϕ + 3.60 [E_k(λ/2)=3.60eV]

→ 2 hc/λ = ϕ + 3.6

hc/λ = ( ϕ + 3.6 )/2 (2)

From eqns 1 & 2 ,we have ϕ + 1.12 = ( ϕ + 3.6 )/2

2 ϕ + 2.24 = ϕ + 3.6

ϕ = 1.36 eV

The work function of the given metal is 1.36 eV (answer) .

genius_generous answered 2 years ago

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