Question

if x is the radius of first bohr's orbit of the hydrogen atom.then the ratio of the radius of second,fourth and sixth orbit is

Answer 1

Answer:

The ratio of the radius of second,fourth and sixth orbit is 1:4:9.

Explanation:

Formula used for the radius of the $n^{th}$ orbit will be,

$r_n=\frac{n^2\times 52.9}{Z}$   (in pm)

where,

$r_n$ = radius of $n^{th}$ orbit

n = number of orbit

Z = atomic number

Given that ,x is the radius of first Bohr's orbit of the hydrogen atom

= $r_1=x=\frac{1^2\times 52.9}{1}$

$r_2=\frac{2^2\times 52.9}{1}=4x$

$r_4=\frac{4^2\times 52.9}{1}=16x$

$r_6=\frac{6^2\times 52.9}{1}=36x$

$r_2:r_4:r_6$

$4x:16x:36x=1:4:9$

The ratio of the radius of second,fourth and sixth orbit is 1:4:9.