Question

The ratio of radii of first, second and third orbits of hydrogen atom is:

• A. $1:4:9$
• B. $1:3:6$
• C. $2:4:6$
• D. $1:2:3$

Answer 1

The correct option is A $1:4:9$

The radius of Bohr's orbit in hydrogen and hydrogen-like species can be calculated by using the following formula:

$r=\frac{n^2{h}^2}{4\pi m{e}^2}\times \frac{1}{Z}=0.529\times \frac{n^2}{Z}{A}^o$

Where :
n = principal quantum number of orbit. ; Z = atomic number
Hence, $r\propto n^2\because z=1$ as it is a Hydrogen atom

for 1st orbital; $r=1$
for second orbital; $r=4$
for the third orbital; $r=9$

So, the ratio for Bohr's first, second and third orbit of Hydrogen is $1:4:9$.