A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u1 and u2, respectively. If the ratio u1 : u2 = 2 : 1 and hc = 1240 eV nm, the work function of the metal is nearly

Engineering

Physics

Photoelectric Effect Einsteins Equation

Question

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u₁ and u₂, respectively. If the ratio u₁ : u₂ = 2 : 1 and hc = 1240 eV nm, the work function of the metal is nearly

3.2 eV

2.5 eV

3.7 eV

2.8 eV

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$\frac{1}{2} {mu}_{1}^{2} = \frac{1240}{248} - ϕ$

$\frac{1}{2} m \times \frac{u_{1}^{2}}{4} = \frac{1240}{310} - ϕ$

$\frac{5}{4} - \frac{ϕ}{4} = 4 - ϕ$

$\frac{3 ϕ}{4} = \frac{4 - 5}{4} = \frac{11}{4}$

$ϕ = \frac{11}{3} eV = 3 .66 eV$