Question

A student of classical physics says, "A charged particle. like an electron orbiting in a simple atom. shouldn't have only certain stable energies: in fact, it should lose energy by electromagnetic radiation until the atom collapses." Answer these two complaints qualitatively. appealing to as few fundamental claims of quantum mechanics as possible.

Short answer

In most of the orbits, the angular momentum is not conserved and hence energy is lost in the form of radiation in overcoming the torque. But there are certain orbits for which the angular momentum is conserved and hence no energy loss occurs in these orbits. These are the stable orbits.

Step-by-step solution

Concept of angular momentum

According to the Bohr model, the electron cannot have any value of energy, as most of the energy levels are unstable. For an energy level to be stable, the necessary condition is that the angular momentum of the electron at that level should be the integral multiple of modified Planck’s constant $\left(\hslash \right)$.

Qualitative Explanation

In classical physics, a particle has a definite boundary and occupies a fixed amount of space. It is also a common observation that a moving charged particle emits energy in the form of electromagnetic radiation. This happens because in most of the orbits, the angular momentum of the electron is not conserved and hence energy is lost in the form of radiation as the work is done in overcoming the torque.

There are a few orbits in which the angular momentum is an integral multiple of modified Planck’s constant and hence is conserved. No torque is acting on the electron and hence no energy loss occurs. These are the stable orbits.

Conclusion

It is the conservation of angular momentum that decides whether the energy loss occurs or not. In unstable orbits, the angular momentum is not conserved, hence energy loss occurs. On the other hand, in stable orbits, the angular momentum of the electron is conserved, hence no energy loss occurs.