Question

The ratio of the radii of the first three bohr orbits for hydrogen atom is:

• A. $1:0.05:0.33$
• B. $1:2:3$
• C. $1:4:9$
• D. $1:8:27$

Answer 1

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

We know,
$r_n=r_o\times \frac{n^2}{Z}$,
where $r_o$ is the radius of first orbit
n = orbit number, Z = Atomic number
Let the radius of $1^{st}$, $2^{nd}$ and $3^{rd}$ orbit be $r_1:r_2:r_3$
So, ratio of radii of first three orbits,
$r_1:r_2:r_3=n_1^2:n_2^2:n_3^2$ = $1:4:9$