Q.Which one of the following cannot emit radiation and why? Excited nucleus, excited electron.

The key idea is that an excited nucleus can emit radiation (gamma rays) when it de-excites, while an excited electron in an atom cannot emit radiation on its own — it must be bound to a nucleus to produce photons via electronic transitions.

Reasoning:

1. An excited nucleus has excess energy and can return to a lower energy state by emitting a gamma photon. This is nuclear radiation.
2. An excited electron in free space (unbound) cannot emit radiation because it has no quantised energy levels to transition between — it simply carries kinetic energy. …

Let’s unpack this carefully. The question asks which of the two — an excited nucleus or an excited electron — cannot emit radiation, and why. The answer hinges on what “excited” means and what kind of system we’re dealing with.

1. What does “excited” mean?

   An excited system has more energy than its ground state (the lowest possible energy). To emit radiation (typically a photon), the system must drop to a lower energy level. The emitted photon carries away the energy difference.

2. Excited nucleus

   A nucleus can exist in excited states (higher energy configurations of protons and neutrons). When it de-excites, it emits a gamma-ray photon. This is a well-known process in nuclear physics — gamma decay. So an excited nucleus can emit radiation.

3. Excited electron — the critical distinction

   An electron can be excited in two very different contexts:

   • Bound electron (in an atom): It can jump to a higher orbital. When it falls back, it emits a photon (e.g., visible light). So a bound excited electron can emit radiation.
   • Free electron (not bound to any atom): A free electron has a continuous energy spectrum — it can have any kinetic energy. There is no “ground state” for a free electron; its energy can be arbitrarily low (approaching zero kinetic energy). If a free electron is “excited” (has extra kinetic energy), it cannot spontaneously emit a photon and drop to a lower energy because that would violate conservation of energy and momentum simultaneously. A free electron cannot emit a photon in isolation — it needs a third body (like a nucleus) to absorb recoil momentum. This is why free electrons do not emit radiation on their own.

4. Why the free electron cannot emit …

Method: Testing Whether an Isolated Excited System Can Emit a Single Photon

Use this whenever a question asks whether some excited system — a nucleus, a bound electron, or a free particle — can spontaneously emit radiation on its own.

Steps

Step 1: Check whether the system has a lower-energy state to fall into

Emission of a photon requires the system to drop from its current (excited) energy to some lower, well-defined energy state. A bound system — like a nucleus with discrete excited levels, or an electron bound in an atom's orbitals — has such discrete lower states available. A completely free particle (not bound to anything) instead has a continuous range of possible kinetic energies, with no discrete "floor" state to transition into in the same sense.

Step 2: Apply conservation of energy AND momentum together, not just energy

For an isolated system to emit a single photon, both energy and momentum must balance simultaneously. Suppose a free particle of mass $m$ moving at speed $v$ emits a photon of energy $h f$:

Solving these two equations together forces $f = 0$ — i.e., no real photon can be emitted by a single free particle acting alone, because there's no third body present to absorb the leftover recoil momentum.

Step 3: Contrast with a bound system …