Question

Ratio of minimum to maximum wavelength of radiation emitted by transition of an electron

Answer 1

Energy of radiation corresponding to between two energy levels, n₁ and n₂ is given by

E =13.6 {(1/n₁²) - (1/n₂²)}

At n₁ = 1 and n₂ = 2, E is minimum

Thus E (minimum) = 13.6(1/1 -1/4) eV

= 13.6 × (3/4) eV

At n₁ = 1 and n₂ = ∞ E is maximum. In this case atom is ionized

Thus E(max) = 13.6 (1 -1/∞) = 13.6 eV

Now the ratio of

(E min/E max) = 3/4

(hc/λ max)/(hc/λ min) =3/4

(λ min/λ max) = 3/4