91Ó°ÊÓ

The speed of electron is v = 0.992 c

The distance travelled by electron in chamber is d = 0.20 cm

The wavelength of light for observer on Earth is calculated by using the formula for Doppler effect in light and color of light is decided by wavelength of light.

a) The time taken by electron to cover distance is given as:

$t=\frac{d}{v}$

Here, c is the speed of light and its value is $3×{10}^{8}m{s}^{-1}$.

Substitute all the values in the above equation.

$t=\frac{\left(20cm\right)\left({\displaystyle \frac{1cm}{100cm}}\right)}{0.992c\left({\displaystyle \frac{3×{10}^{8}m{s}^{-1}}{c}}\right)}$

$t=6.72×{10}^{-10}s$

Therefore, the time taken by electron to cover distance is $6.72×{10}^{-10}s$.

b) The distance fallen by electron in chamber is given as:

$y=\frac{1}{2}{g}^2$

Here, g is the gravitational acceleration and its value is $9.8m{s}^{-2}$.

Substitute all the values in the above equation.

$$\begin{gathered} y=\frac{1}{2}\left(9.8\text{m}/{\text{s}}^2\right){\left(6.72×{10}^{-10}\text{s}\right)}^2 \\ =2.213×{10}^{-18}\text{m} \end{gathered}$$

Therefore, the distance fallen by electron in chamber is $2.213×{10}^{-18}m$.

c)

As the distance fallen by the electron is very less compared to horizontal distance of electron in chamber due to negligible effect of gravity on electron and very high speed of electron, so the laboratory can be considered as inertial frame for experiment.

Therefore, the laboratory can be considered as inertial frame for experiment.