Question

electrons from n=2 to n=1 in hydrogen atom is made to fall on a metal surface with function 1.2ev.the maximum velocity of photo electrons emitted is nearly equal to

Answer 1

Using the Rydberg Equation,

1/λ = R(1/n₁² - 1/n₂²)

ν/c = R(1/1 - 1/4)

1/λ = R(3/4)

∴ λ = 4/3R

∴ λ = 4/3 × 912 × 10⁻¹⁰ m.  [Since, R = 1/912 A°.]

∴ λ = 1.216 × 10⁻⁷ m.

Now,

ν = 3 × 10⁸/1.216 × 10⁻⁷

ν = 2.46 × 10¹⁵

hν = 6.67 × 10⁻³⁴ × 2.46 × 10¹⁵ = 1.64 × 10⁻¹⁸ J.

∴ hν = hν₀ + K.E.

K.E.  = hν - hν₀

K.E. = 1.64 × 10⁻¹⁸ - 1.2eV

K.E. = 1.64 × 10⁻¹⁸ - 1.2 × 1.6 × 10⁻¹⁹

K.E. = 1.64 × 10⁻¹⁸ - 0.92 × 10⁻¹⁸

K.E. = 0.72 × 10⁻¹⁸ J.

1/2 mv² = 0.72 × 10⁻¹⁸

v² = 1.44/9.1 × 10³¹⁻¹⁸

∴ v² = 0.158 × 10¹³

∴ v = 1.25 × 10⁶ m/s.

Hope it helps.