Problem 5.200

A free electron is located in the field of a monochromatic light wave. The intensity of light is $I=150 \mathrm{~W} / \mathrm{m}^{2}$, its frequency is $\omega=3.4 \cdot 10^{15} \mathrm{~s}^{-1}$. Find: (a) the electron's oscillation amplitude and its velocity amplitude; (b) the ratio $F_{m} / F_{e}$, where $F_{m}$ and $F_{e}$ are the amplitudes of forces with which the magnetic and electric components of the light wave field act on the electron; demonstrate that that ratio is equal to $\frac{1}{2} v / c,$ where $v$ is the electron's velocity amplitude and $c$ is the velocity of light.

Instruction. The action of the magnetic field component can be disregarded in the equation of motion of the electron since the calculations show it to be negligible.