Question

State Bohr’s second postulate and mention its significance.

Hint:

Higher energy levels in atoms behave almost continuously, which is why ionization limit corresponds to \(n \to \infty\).

Answer 1

Bohr’s second postulate and its significance

Step 1: Statement of Bohr’s second postulate
Bohr proposed that electrons in an atom do not lose energy continuously while revolving in certain permitted orbits. Only those orbits are allowed in which the angular momentum of the electron is quantized. Mathematically: \[ m v r = \frac{n h}{2\pi}, \quad n = 1,2,3,\ldots \] where:
• \(m\) = mass of electron
• \(v\) = velocity of electron
• \(r\) = radius of orbit
• \(h\) = Planck’s constant
• \(n\) = principal quantum number

Step 2: Physical significance
This postulate has deep physical implications:
• It restricts electron motion to discrete orbits, preventing collapse into the nucleus.
• It explains atomic stability because electrons in allowed orbits do not radiate energy.
• It leads to quantized energy levels, which directly explains the line spectra of hydrogen. Thus, the second postulate is the foundation of quantization in atomic structure.