An electron in a hydrogen atom is found to be moving in a circular orbit of radius…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

An electron in a hydrogen atom is found to be moving in a circular orbit of radius

2.12\times10^{-10}\,\text{m}

with a speed of

9.72\times10^{5}\,\text{m\,s}^{-1}

. Take the mass of the electron

m_e = 9.11\times10^{-31}\,\text{kg}

and Planck’s constant

h = 6.63\times10^{-34}\,\text{J\,s}

. (i) Calculate the orbital angular momentum

L

of the electron. (ii) Determine the principal quantum number

n

for this orbit by comparing the calculated

L

with the permitted values. (iii) State, with reasoning, whether this orbit is one of the allowed stationary states predicted by Bohr’s model.