Question

What is the mathematical formula for third postulate of Bohr's atomic model?

Hint:

Bohr’s quantization applies to angular momentum; use \( \frac{h}{2\pi} \) for reduced Planck’s constant.

Answer 1

Bohr’s third postulate states that the angular momentum of an electron in a stable orbit is quantized. The angular momentum \( L = mvr \) (where \( m \) is electron mass, \( v \) is velocity, \( r \) is orbit radius) is an integer multiple of \( \frac{h}{2\pi} \): \[ mvr = n \frac{h}{2\pi}, \] where \( n \) is the principal quantum number and \( h \) is Planck’s constant.
Answer: \( mvr = \frac{n h}{2\pi} \).