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Question
Answer the following question.
Calculate the orbital period of the electron in the first excited state of the hydrogen atom.
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Solution
`r = 0.53n^2/z xx 10^-10`m
for first excited state n = 2
`r = 0.53 2^2/1 xx 10^-10`
`r = 2.12 xx 10^-10`m
ν = `ν_0 xx Z/n` m/s
`ν = 2.188 xx 10^6 xx Z/n` m/s
For first excited state, n = 2, Z = 1 for hydrogen atom
∴ ν = `2.188 xx 10^6 xx 1/2` m/s
⇒ `ν = 1.094 xx 10^6` m/s
∵ Orbital period = `(2pir)/ν = (2 xx 3.14 xx 2.12 xx 10^-10)/(1.094 xx 10^6)`
⇒ Orbital period = `1.22 xx 10^-15`sec.
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