Question

Using Bohr's theory, calculate the radius(in $\mathring{A} $ ) of the tenth orbit in the hydrogen atom.

Express the answer to the nearest integer value.

Answer 1

The radius of Bohr orbit can be given as:
$r_{n}=a_{0}\times \frac{n^{2}}{Z},where,a_{0}=\text{Bohr radius}=0.529\mathring{A} $
For hydrogen atom, $Z=1$
$r _{10}= a _{0} (10=100 a _{0} r _{10}=100 \times 0.529=52.9 \mathring{A} \simeq 53 \mathring{A}$