The radius of the innermost electron orbit of a hydrogen atom is `5.3 xx 10^(–11) m`. What are the radii of the n = 2 and n =3 orbits?

Explanation

`r_(0)=a_(0)=5.3xx10^(-11)m`
`:. In n=2,r ^(2)=?`
In `n=3, r^(3)=?`
`rArr` Radius of electron in `n^(th)` orbit in hydrogen atom `r_(n)=n^(2)r_(0)`
Radius in n=2 orbit,
`r_(2)=(2)^(2)xx5.3xx10^(-11)`
`=4xx5.3xx10^(-11)`
`:.r_(@) =2.12xx10^(-10)m`
Radius in n=3 orbit,
`r_(3)=(3)^(2)xx5.3xx10^(-11)`
`=9xx5.3xx10^(-11)`
`:.r_(3)=4.77xx10^(-10)m`