Question

In the hydrogen spectrum, λ be the wavelength of first transition line of Lyman series. The wavelength difference will be "aλ" between the wavelength of 3rd transition line of the Paschen series and that of 2nd transition line of Balmer series where a = ______.

Answer 1

$\frac 1λ=R_H(\frac {1}{1^2}−\frac {1}{2^2)}$

$\frac {1}{λ_3}=R_H(\frac {1}{3^2}−\frac {1}{6^2)}$

$\frac {1}{λ_2}=R_H(\frac {1}{2^2}−\frac {1}{4^2)}$
Wavelength difference $λ_3–λ_2=aλ$
$a=5$

So, the answer is $5$.