Question

The ratio of radii of first orbit of hydrogen atom and the second orbit of singly ionised helium atom will be

• A. $1:2$
• B. $4:1$
• C. $1:4$
• D. $8:1$

Answer 1

The correct option is A $1:2$

For hydrogen and hydrogen like atoms,
$r_n\propto \frac{n^2}{Z}$
where, $r_n$ is the radius of $n^{th}$ orbit of revolution of electron, Z is the atomic number.
For hydrogen atom, Z = 1. Hence, radius of first orbit is: $r_h=\frac{1^2}{1}=1$
Also, or helium atom, Z = 2. Hence, radius of second orbit is: $r_{he}=\frac{2^2}{2}=2$
Therefore, $\frac{r_h}{r_{he}}=\frac{1}{2}$