Question

An electron in the n = 6 level of an H atom emits a photon of wavelength 2626 nm. To what energy level does it move?

Answer 1

Answer on Question #45492, Physics, Atomic Physics

An electron in the $n = 6$ level of an H atom emits a photon of wavelength 2626 nm. To what energy level does it move?

Solution:

We use the Rydberg formula for hydrogen

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

Where $\lambda$ is the wavelength of electromagnetic radiation emitted in vacuum,

R is the Rydberg constant, approximately $1.097 \times 10^{7} \mathrm{~m}^{-1}$,

$n_1$ and $n_2$ are integers greater than or equal to 1 such that $n_1 < n_2$.

In our case $\lambda = 2626 \times 10^{-9} \mathrm{~m}$, $n_2 = 6$ and $n_1 = ?$.

$$\frac {1}{n _ {1} ^ {2}} = \frac {1}{R \lambda} + \frac {1}{n _ {2} ^ {2}} = \frac {1}{1.097 \cdot 10^{7} \cdot 2626 \cdot 10^{-9}} + \frac {1}{6 ^ {2}} = 0.0347 + \frac {1}{36} = 0.0625$$

Thus,

$$n _ {1} ^ {2} = \frac {1}{0.0625} = 16$$

So,

$$n _ {1} = 4$$

Answer: $n_1 = 4$.

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