Question

If the series limit frequency of the Lyman series is v_L, then the series limit frequency of the Pfund series is:

• A. $\frac{v_L}{16}$
• B. $\frac{v_L}{25}$
• C. $25v_L$
• D. $16v_L$

Answer 1

The correct option is B

$\frac{v_L}{25}$

Step 1: Given Data

Series limit frequency of Lyman series is $v_L$.

Let series limit frequency of Pfund series be $v_p$.

Step 2: Formula Used

Frequency,

$\nu =\frac{c}{\lambda }$

$\lambda$ is the wavelength, $c$ is speed of light

Rydberg formula,

$$\begin{gathered} \frac{1}{\lambda }=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \\ v=\frac{c}{\lambda } \\ v=c\times R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \end{gathered}$$

where $R$ is the Rydberg constant and $n_{1}and{n}_2$ are the final and initial energy levels.

Step 3: Calculation

For Lyman series, $n_1=1and{n}_2=\infty$

so,

$$\begin{gathered} v_L=Rc\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \\ {v}_L=Rc\left[\frac{1}{1^2}-\frac{1}{\infty }\right] \end{gathered}$$

therefore, $v_L=Rc$

now, for Pfund series, $n_1=5and{n}_2=\infty$

$$\begin{gathered} V_p=Rc\left[\frac{1}{5^2}-\frac{1}{\infty }\right] \\ =\frac{Rc}{25} \\ =\frac{v_L}{25} \end{gathered}$$

Hence, the Pfund series is $\frac{v_L}{25}$.