Bohr's model enables us to derive the energy of an electron revolving in nth orbit. For H-atom and hydrogen like species :
`E_n = (2 pi^2 m e^4 Z^2)/(n^2 h^2)`
or `= - (13.6 Z^2)/(n^2) eV "atom"^(-1) = (21.8 xx 10^(-19) Z^2)/(n^2) J "atom"^(-1)`
This helps to calculate the radius of an orbit,
`r_n = (0.529 n^2)/(Z) Å`
Bohr's model also explains the occurrence of different spectral lines. The wavelengths of difference line can be given as :
`1/lambda = barv ("in" cm^(-1)) = R (1/(n_1^2) - 1/(n_2^2))`
`R = 109678 cm^(-1) and n_2 > n_1`.
What is the ratio of radius of 4th orbit of hydrogen and 3rd orbit of `Li^(2+)` ion ?

Explanation

To find the ratio of the radius of the 4th orbit of hydrogen (H) and the 3rd orbit of the lithium ion (Li²⁺), we will use the formula for the radius of an electron in a given orbit according to Bohr's model:

\[ r_n = \frac{0.529 \, n^2}{Z} \, \text{Å} \]

### Step 1: Calculate the radius of the 4th orbit of hydrogen (H)
For hydrogen, the atomic number \( Z \) is 1. We need to substitute \( n = 4 \) into the formula:
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