What is the importance of the number 137?

Answer 1

I suspect you are referring to the so-called fine structure constant, whose value is about 1/137 (although it varies with energy, 1/137 is the zero energy value). It describes the strength of the electromagnetic force, one of the four fundamental forces of nature, making it quite important.

It describes for example how often an electron would emit a photon, the strengths of electric and magnetic fields and molecular bonds.

It is also dimensionless, so the number is the same regardless of which units you happen to use.

Answer 2

The number 137 is important in physics as it is approximately the reciprocal of the fine-structure constant, a dimensionless physical constant that characterizes the strength of the electromagnetic interaction between elementary charged particles. It is a fundamental constant that governs the behavior of subatomic particles and plays a key role in quantum mechanics.