Q7
Show that the radius of the orbit in hydrogen atom varies as n², where n is the principal quantum number of the atom.
Solution
According to Bohr's second postulate, mvr = nh/2π, where m is the mass of an electron, v is its velocity, and r is the radius of its orbit around the nucleus.
As a result, v = nh/2πmr
The electrostatic force of attraction between electron and nucleus provides the centripetal force in this case.
Therefore, mv²/r = k(Ze)(e)/r²
⇒ r = kZe²/mv²
Putting the value of v:
r = n²h²/4π²mkZe²
Hence, r ∝ n²
