Now consider an excited‑state hydrogen atom. What is
Answered question
2022-04-10
Now consider an excited‑state hydrogen atom. What is the energy of the electron in the 𝑛=5 level
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Question

Now consider an excited‑state hydrogen atom. What is the energy of the electron in the 𝑛=5&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;level

nick1337 · Accepted Answer

According to Rydbery equation for calculation of energy

$E = \frac{- h c R n}{n^{2}}$

h $\to$ Plank's constant = 6.626 $\times$ $10^{- 34} m^{2}$ kg/s

c - speed of ight = 3 $\times$ $10^{8}$ m/s

$R_{n}$ - Rydbery contact = 1097 $\times$ $10^{7} m^{2}$

For Grand state n=1

$E_{1} = (- 6.626 \times 10^{- 34} m^{2} k g / s) \times (3 \times 10^{8} m / s) (1.097 \times 10^{7} m^{2}) {(1)}^{2}$

$= - 21.806 \times 10^{- 19} k g m^{2} / s^{2}$

[ $k g / s^{2} = J / m$ ]

Thus, $E_{1} = - 2.1086 \times 10^{- 18} J$

for excited state, n=5

$E_{5} = (- 6.626 \times 10^{- 34} m^{2} k g / s) \times (3 \times 10^{8} m / s) (1.09 \times 10^{7} m^{2}) {(5)}^{2}$

$= - 0.08722 \times 10^{- 18} J$

$= - 8.72 \times 10^{- 20} J$

Now consider an excited‑state hydrogen atom. What is