Question

Calculate the ratio of radii of second and third bohr orbit of H-atoms

Answer 1

The correct answer is : $\frac{4}{9}$
The radii of the Bohr orbits in hydrogen atom are given by the formula:
$r_n = \frac{(n^2 * h^2 * ε₀) } {(π * m * e^2)}$
where r_n is the radius of the nth Bohr orbit, n is the principal quantum number, h is the Planck's constant, ε₀ is the permittivity of free space, m is the mass of the electron, and e is the charge of the electron.
The ratio of radii of the second and third Bohr orbits can be calculated by substituting n=2 and n=3 in the above formula and taking the ratio:
$\frac{r_2}{ r_3} = \frac{\frac{(2^2 * h^2 * ε₀)}{(π * m * e^2)}}{ \frac{(3^2 * h^2 * ε₀)}{ (π * m * e^2)}}$
$= \frac{4}{9}$
Therefore, the ratio of radii of second and third Bohr orbit of H-atoms is $\frac{4}{9}$