In the ground state of hydrogen atom orbital radius is `5.3 xx 10^(-11)`m.
The atom is excited such that atomic radius becomes `21.2 xx 10^(-11) m`.
What is the principal quantum number of the excited state of atom ?

Explanation

To find the principal quantum number of the excited state of a hydrogen atom when the radius changes from \(5.3 \times 10^{-11} \, \text{m}\) to \(21.2 \times 10^{-11} \, \text{m}\), we can use the formula for the radius of the nth orbit of a hydrogen atom:

\[ r_n = n^2 \cdot r_1 \]

where:
- \(r_n\) is the radius of the nth orbit,
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