Question

Radiation of some definite frequency are either absorbed or emitted by the atoms. Explain the reason.

Hint:

Atomic energy levels are discrete; a photon is absorbed or emitted only when \( h\nu \) equals the gap \( E_2 - E_1 \).

Answer 1

Step 1 (Concept of energy levels): According to Bohr's atomic model, the electron in an atom can occupy only certain fixed orbits, each having a definite (discrete/quantized) energy \( E_1, E_2, E_3, \ldots \). The electron cannot have any energy in between these allowed values.

Step 2 (Transition rule): An atom absorbs energy when the electron jumps from a lower level \( E_1 \) to a higher level \( E_2 \), and emits energy when it falls back from \( E_2 \) to \( E_1 \). The energy exchanged is exactly the difference between the two levels:
\[ h\nu = E_2 - E_1 \]

Step 3 (Reason for definite frequency): Since \( E_1 \) and \( E_2 \) are fixed, the difference \( (E_2 - E_1) \) is fixed, so the frequency
\[ \nu = \frac{E_2 - E_1}{h} \]
can take only definite values. Therefore an atom absorbs or emits radiation only of certain definite frequencies.

\[\boxed{\nu = \dfrac{E_2 - E_1}{h}: \text{fixed energy levels give fixed frequencies.}}\]