For hydrogen atom, λ₁ and λ₂ are the wavelengths corresponding to transitions 1 and 2 shown in the figure. The ratio λ₁/λ₂ is x/32. The value of x i $s ______.$

Question

For hydrogen atom, λ₁ and λ₂ are the wavelengths corresponding to transitions 1 and 2 shown in the figure. The ratio λ₁/λ₂ is x/32. The value of x i s ______.

G1 Physics · Accepted Answer

Transition 1 is 3→1: 1/λ₁ = R(1-1/9)=8R/9. Transition 2 is 2→1: 1/λ₂ = R(1-1/4)=3R/4. Therefore λ₁/λ₂ = ( 3 4 \frac{3}{4} 4 3 ​ )/(8/9)=27/32, so x=27.