Question

An electronic transition in the Paschen series of hydrogen involves an electron dropping from the n=5 level to the n=3 level. What is the wavelength for this transition? Express your final result in micrometers. (SHOW ALL WORK)

Answer 1

Answer on Question #76390, Chemistry / General Chemistry

An electronic transition in the Paschen series of hydrogen involves an electron dropping from the $n=5$ level to the $n=3$ level. What is the wavelength for this transition? Express your final result in micrometers. (SHOW ALL WORK)

Answer

We should use the Rydberg equation:

$$\frac {1}{\lambda} = R _ {\infty} \left(\frac {1}{n _ {f} ^ {2}} - \frac {1}{n _ {i} ^ {2}}\right)$$

where $R_{\infty} = 1.09737316 \times 10^{7} \, \text{m}^{-1}$,

$n_f = 3, n_i = 5$, then

$$\frac {1}{\lambda} = 1.09737316 \times 10^{7} \left(\frac {1}{3^{2}} - \frac {1}{5^{2}}\right) = 7.8 \times 10^{5}$$ $$\lambda = \frac {1}{7.8 \times 10^{5}} = 1.28 \times 10^{-6} \, (\text{m}) = 1.28 \, (\mu\text{m})$$

Answer: $1.28 \, \mu\text{m}$