Question

The radius of the innermost electron orbit of a hydrogen atom is $5.3×10^{–11} m$. What are the radii of the n=2 and n=3 orbits?

Answer 1

The radius of the innermost orbit of a hydrogen atom, $r_1=5.3×10^{-11}m.$
Let $r_2$ be the radius of the orbit at n=2. It is related to the radius of the innermost orbit as:
$r_2=(n)^2r_1$
$=4×5.3×10^{-11}=2.12×10^{-10}m$
For n=3,we can write the corresponding electron radius as:
$r_3=(n)^2r_1$
$=9×5.3×10^{-11}=4.77×10^{-10}m$
Hence, the radii of an electron for n=2 and n=3 orbits are $2.12×10^{-10}m$ and $4.77×10^{-10}m$ respectively.