Question

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

Answer 1

Step 1: Find radius for n = 2 orbit. Given, radius of innermost electron orbit $r_0=5.3\times {10}^{-11}m$
Radius for $n^{th}$ orbit is given by,
$r_n=r_0{n}^2$
For n = 2
Radius of the orbit $r_2=r_0(2{)}^2$
$r_2=(5.3\times {10}^{-11})(2{)}^2$
$r_2=2.12\times {10}^{-10}m$
Step 2: Find radius for n =3 orbit.
For n = 3
Radius of the orbit, $r_3=r_0(3{)}^2$
$r_3=(5.3\times {10}^{-11})(3{)}^2$
$r_3=4.77\times {10}^{-10}m$
Final answer:
$2.12\times {10}^{-10}m;4.77\times {10}^{-10}m$