Question

Calculate the ratio of the radius of 1 st bohr orbit of H atom to that of 4th bohr orbit

Answer 1

Dear student,

Radius of the orbit = $r=\left(\frac{n^2{h}^2}{4{\mathrm{\pi }}^2{\mathrm{me}}^2}\right)\times \frac{1}{Z}=0.529\times \frac{n^2}{Z}{A}^o$
where n = Number of shell
Z = Atomic number.

Ratio of radius:

$\left(\frac{r_1}{r_2}\right)=\left(\frac{0.529\times {\displaystyle \frac{{n_1}^2}{Z}}}{0.529\times {\displaystyle \frac{{n_2}^2}{Z}}}\right)$
n₁ = 1
n₂ = 4

$\left(\frac{r_1}{r_2}\right)=\left(\frac{{n_1}^2}{{n_2}^2}\right)$
= $\left(\frac{1^2}{4^2}\right)=\left(\frac{1}{16}\right)$
The ratio of radius = 1:16

Regards