The radii of 2 bohr orbits are in the ratio 4:9?

Question

Answer

Explanation:

Bohr Model of the Atom:

The Bohr model of the atom describes electrons orbiting the nucleus in specific energy levels or shells.
Each orbit has a specific radius and energy associated with it.

Relation between Radii of Bohr Orbits:

The radii of Bohr orbits are given by the formula: $r_n = \frac{n^2h^2}{4\pi^2mkZe^2}$, where n is the principal quantum number, h is the Planck's constant, m is the mass of the electron, k is the Coulomb constant, Z is the atomic number, and e is the charge of an electron.
Given that the radii of two Bohr orbits are in the ratio 4:9, we can write: $\frac{r_1}{r_2} = \frac{4}{9}$.
Substitute the values of the radii of the two orbits in the formula and simplify the ratio to find the relation between the principal quantum numbers of the two orbits.

Conclusion:

By analyzing the ratio of the radii of two Bohr orbits, we can determine the relationship between the principal quantum numbers of the orbits.
This helps in understanding the electron distribution in an atom and the energy levels associated with each orbit.