#### Question

Numerical

**Answer the following question.**

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

#### 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.

Concept: Bohr'S Model for Hydrogen Atom

Is there an error in this question or solution?

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