Name: Bohr Atom Model: Frequency of Emitted Radiation
Uploaded: 2019-07-19
Duration: 3 min 54 s
Description: Electrons jump in different energy levels. Let's understand how we can calculate the frequency of emitted and absorbed radiation as electrons transition into...

Question

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

Accepted Answer

The radius of the $n^{th}$ orbit of the hydrogen and hydrogen like atoms is given by

$r_{n} = \frac{0.53 n^{2}}{Z} A °$

where $Z$ is atomic number.

The velocity of the electron in $n^{th}$ orbit of hydrogen and hydrogen like atoms is given by

$v_{n} = \frac{2.2 \times 10^{6} \times Z}{n} m s^{- 1}$

The orbital period of the electron is given by

$T = \frac{2 {πr}_{n}}{v_{n}}$

Substituting the values from above, we get,

$T = \frac{2 π \times n \times 0.53 \times n^{2} \times 10^{- 10}}{2.2 \times 10^{6} \times Z \times Z} = \frac{1.06 {πn}^{3} \times 10^{- 10}}{2.2 \times 10^{6} \times Z^{2}}$

For hydrogen atom, $Z = 1$ and for first excited state $n = 2$ .

Put these values in above equation, we get

$T = \frac{1.06 π {(2)}^{3} \times 10^{- 10}}{2.2 \times 10^{6}} = 12.1 \times 10^{- 16} s .$

So, the orbital period of the electron in the first excited state is $1.21 \times 10^{- 15} s$ .

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

Important Questions on Atoms

Learn and Prepare for any exam you want !