Why the Classical Atom is Unstable (Spiralling Electron)
Physics · Atoms · NEET
In Rutherford's model the electron moves in a circle, so it is always accelerating (centripetal). Classical electromagnetic theory says any accelerating charge must radiate energy. So the electron keeps losing energy, its orbit shrinks, and it spirals into the nucleus in about 1e-8 second. Memory hook: "moving in a circle = accelerating = radiating = losing energy = falling in." A real atom lives forever, so classical physics fails and Bohr's quantum rules were needed.
In Rutherford's classical model the revolving electron is accelerating, so it radiates electromagnetic energy, its orbit steadily shrinks, and it spirals into the nucleus in about 1e-8 second. This predicted collapse contradicts the observed stability of real atoms.
Your doubts, answered
Why is a revolving electron said to be accelerating even at constant speed?
Acceleration means any change in velocity, and velocity is a vector (speed plus direction). In a circular orbit the direction of motion changes every instant, so the velocity keeps changing even if the speed is constant. This gives centripetal acceleration pointing toward the nucleus. So the electron is always accelerating.
Why does an accelerating electron lose energy?
By classical electromagnetic theory, any accelerating charged particle emits electromagnetic radiation (light). Emitting radiation carries away energy. Since the orbiting electron is accelerating, it must continuously radiate, so its total energy continuously decreases.
Why does losing energy make the electron spiral inward?
For an electron bound to the nucleus, total energy is negative and equals E = -ke^2/2r. As the electron radiates and its energy becomes more negative, the radius r must get smaller. So the orbit keeps shrinking and the electron spirals inward until it hits the nucleus. The estimated collapse time is only about 1e-8 second.
If the classical atom collapses, why do real atoms not collapse?
Real atoms are stable and last forever, which directly contradicts the classical prediction. This failure showed that classical physics cannot be applied at the atomic scale. Bohr fixed it by adding quantum postulates: the electron can only stay in certain fixed orbits (stationary states) and does not radiate while in them.
Why does the planet orbiting the Sun not spiral in, but the electron does?
A planet is neutral and is held by gravity, and gravity does not require the orbiting body to radiate. The electron is a charged particle held by the Coulomb force, and a charged particle that accelerates must radiate electromagnetic energy. That radiation is what makes the electron lose energy and spiral in, while the planet keeps orbiting.
⚠️ The NEET trap ✗ The electron is unstable because it moves at very high speed and gravity pulls it into the nucleus. ✓ Speed and gravity are not the cause. The electron is unstable because it is accelerating (circular motion) and, being a charge, it must radiate electromagnetic energy. This loss of energy shrinks the orbit until it falls in. 🧠 NTA loves the word 'accelerating charge radiates.' If the option does not mention radiation of energy by the accelerating (revolving) electron, it is the wrong reason.
Real NEET questions
2024
Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer.
A · Both Statement I and Statement II are incorrect
B · Statement I is correct but Statement II is incorrect
C · Statement I is incorrect but Statement II is correct
D · Both Statement I and Statement II are correct ✓
Solution: Step 1: Statement I. An atom has equal numbers of protons (positive) and electrons (negative), so their charges cancel and the atom is electrically neutral. Statement I is correct. Step 2: Statement II. Experimentally, atoms of each element are stable and give a characteristic line spectrum unique to that element. Statement II is correct. Step 3: Note the key point for this concept. It is exactly this observed stability and characteristic spectrum that the classical Rutherford model could NOT explain, because a revolving electron should radiate and spiral in. Both statements are true, so the answer is D.
Solved Atoms NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
A standard estimate gives about 1e-8 second (roughly 10 nanoseconds) for the electron to spiral from the normal orbit into the nucleus. This tiny lifetime clashes with real atoms, which are permanently stable.
What does the spiralling electron problem prove?
It proves that classical electromagnetic theory cannot be applied to the atom. This failure of the Rutherford model directly led to Bohr's model, where electrons occupy fixed stationary orbits and do not radiate.
Does the electron radiate a continuous or line spectrum in the classical picture?
Classically it would emit a continuous spectrum, because as the orbit shrinks the frequency of revolution keeps changing smoothly, so the emitted frequency would vary continuously. Real atoms give sharp line spectra, another failure of the classical model.
Is the initial frequency of the emitted light calculable classically?
Yes. NCERT Example 12.4 shows that classically the light frequency equals the electron's revolution frequency, giving about 6.6e15 Hz for hydrogen. But because the orbit shrinks, this frequency would keep rising, producing a continuous spectrum, which is not observed.
What are the two main failures of the Rutherford model?
One, it predicts atoms are unstable because the accelerated revolving electron must spiral into the nucleus. Two, it cannot explain the characteristic line spectra of different elements.
