Question

If the ionisation potential for hydrogen atom in a sample is 122.4 eV, then the series limit of the Paschen series for this atom is:

• A. $\frac{R}{3^2}$
• B. $\frac{R}{3^3}$
• C. $\frac{3^{2}R}{4^2}$
• D. $3^{2}R$

Answer 1

The correct option is A $\frac{R}{3^2}$

The expression for the frquency of emitted radiation is $\nu =R{Z}^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$.
For H atom, $Z=1$
For paschen series, $n_1=3$
For the series limit, $n_2=\infty$
Hence, the above expression becomes $\nu =R(1{)}^2\left(\frac{1}{3^2}-\frac{1}{{\infty }^2}\right)=\frac{R}{9}$.