Question

Answer the following question.
Calculate the orbital period of the electron in the first excited state of the hydrogen atom.

Answer 1

`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.