Write the value of Bohr’s radius.

The Bohr radius ( a o ) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5 . 29177210903 80 × 10 - 11 m .

Define impact parameter.

The impact parameter is defined as the perpendicular distance between the path of a projectile and the center of a potential field created by an object that the projectile is approaching. It is often referred to in nuclear physics (see Rutherford scattering) and in classical mechanics.

Derive an expression for the total energy of an electron in any orbit of a hydrogen atom in accordance with Bohr’s atomic model.

The total energy of an electron in any orbit of a hydrogen atom

Calculate the wavelength of first spectral line of Balmer series for hydrogen. Given that Rydberg constant, R = 1 . 097 x 10 7 m - 1

For the first in Balmer series n 1 = 2 and n 2 = 3 . So, V H R 1 n 1 2 - 1 n 2 2 c m - 1 = 109677 1 ( 2 ) 2 - 1 ( 3 ) 2 c m - 1 = 109677 × 5 36 c m - 1 = 15232 . 9 c m - 1 o r λ = 1 V = 1 15232 . 9 = 6 . 565 × 10 - 5 6561 A .