Derive the velocity of an electron in a hydrogen atom using bohr's model. the electron has a mass of m, charge of (-e) and an orbit radius of r. make sure you explain all the teps including quantization of angular momentum to get full credits

Explanation:

According to Bohr's Theory,

The force of attraction acting between the electron and the nucleus is equal to the centrifugal force acting on the electron.

Thus,

......1

Where, Z is the atomic number or the number of protons

r is the atomic radius

v is the velocity of the electron

is the mass of the electron

Also,

Accoriding to Bohr, the angular momentum is quantized. He states that the angular momemtum is equal to the integral multiple of .

....2

solving r from equation 2, we get that:

Putting in 1 , we get that:

Applying values for hydrogen atom,

Z = 1

Mass of the electron () is 9.1093×10⁻³¹ kg

Charge of electron (e) is 1.60217662 × 10⁻¹⁹ C

= 8.854×10⁻¹² C² N⁻¹ m⁻²

h is Plank's constant having value = 6.626×10⁻³⁴ m² kg / s

We get that: