What does the momentum transferred to a surface by radiation energy E that falls on it normally equal?

When radiation energy falls normally on a surface, it transfers momentum to that surface according to the principles of momentum conservation and the behavior of electromagnetic waves.

The radiation pressure exerted on a surface is a result of the momentum carried by the electromagnetic waves. The momentum ( p ) associated with the energy ( E ) of radiation is given by the relationship ( p = \frac{E}{c} ), where ( c ) is the speed of light in a vacuum.

However, it is essential to consider that when radiation is reflected off a surface, the momentum change is doubled. Specifically, the momentum transferred to the surface is equal to twice the momentum of the incoming radiation. Thus, reflecting radiation that falls normally on the surface would impart not just its original momentum, but also an additional momentum change due to reflection. Therefore, the total momentum transferred becomes ( 2 \times \frac{E}{c} = \frac{2E}{c} ).

This explains why the total momentum transferred to the surface by the radiation energy falling normally is expressed as ( \frac{2E}{c} ). Thus, the understanding of momentum transfer through the behavior of electromagnetic radiation upon incidence and reflection solidifies why this answer is