If an electron is promoted from the first orbit to the third orbit of a hydrogen atom, by how many times will the radius of the orbit be increased?

Explanation

The radius of the 'n' th orbit of an H-atom `r_(n)=(n^(2)h^(2))/(4pi^(2)me^(2))`
Radius of the first orbit `(r_(1))=(1^(2)xxh^(2))/(4pi^(2)me^(2))`
and radius of the third orbit `(r_(3))=(3^(2)xxh^(2))/(4pi^(2)me^(2))`
`therefore (r_(3))/(r_(1))=(3^(2)xxh^(2))/(4pi^(2)me^(2))x(4pi^(2)me^(2))/(h^(2))=9" i.e., "r_(3)=9xxr_(1)`.
`therefore` If the electron moves from the 1st orbit to the 3rd orbit, the radius of the orbit will be increased 9 times.