Problem 11

  In the line spectrum of atomic hydrogen there is also a group of lines known as the Pfund series. These lines are produced when electrons, excited to high energy levels, make transitions to the n = 5 level. Determine (a) the longest wavelength and (b) the shortest wavelength in this series. (c) Refer to Figure 24.9 and identify the region of the electromagnetic spectrum in which these lines are found.

SOLUTION:
(a) The longest wavelength corresponds to the smallest energy, which would occur between the n = 6 and n = 5 states. Using equation 30.14, we get

$$\frac{1}{\lambda} = (1.097 \times 10^7 m^{-1}) \left ( \frac{1}{25} - \frac{1}{36} \right )$$

$$\lambda = 7458 nm$$

(b) The shortest wavelength is the largest energy, or when the electron comes from n = $\infty$ to n = 5

$$\frac{1}{\lambda} = (1.097 \times 10^7 m^{-1}) \left ( \frac{1}{25} \right )$$

$$\lambda = 2279 nm$$

(c) The lines in the Pfund series are in the infrared.