If a is the ratio of the Balmer series-limit wavelength to the wavelength of the first Paschen line, find 36a.
Physics · Atomic Structure and X-rays
JEE Advanced Practice

Question

If a is the ratio of the Balmer series-limit wavelength to the wavelength of the first Paschen line, find 36a.

G1 Physics · Accepted Answer

Step 1: The Balmer-series limit has 1/λ = R(1/2²), so its wavelength is 4/R. Step 2: The first Paschen line is the transition 4→3, so 1/λ = R(1/3²−1/4²)=7R/144, giving wavelength 144/(7R). Step 3: Their ratio is (4/R)/[144/(7R)] = 7/36. Hence 36a = 7.