Question

What will the ratio of the wavelength of the first line to that of the second line of Paschen series of H atom?

• A. $256:175$
• B. $175:256$
• C. $15:16$
• D. $24:27$

Answer 1

The correct option is A $256:175$

For single electron species,

$\frac{1}{\lambda }=R{Z}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

1λ=RZ2(1n12−1n22)$

1.097×107×1For Hydrogen atom, Z = Atomic number = 1

For Paschen series,

$n_1=3$

For first line In Paschen series, $n_2=4$

For second line in Paschen series, $n_2=5$

So, ratio of the wavelength of the first line to that of second line

=$\frac{{\lambda }_1}{{\lambda }_2}=(\frac{1}{3^2}-\frac{1}{5^2})/(\frac{1}{3^2}-\frac{1}{4^2})$

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{256}{175}$