91影视

The wavelength of the X-rays is$位=0.062\text{nm.}$

The wavelengths of aphoton help to determine the speed of electrons in a beam of mono-energetic electrons by using the relation of momentum of the photon.

The relation of thespeed of an electron in a beamis mathematically expressed as:

$\begin{array}{c}v=\frac{p_{photon}}{m_e}\\ =\frac{\left(\frac{h}{位}\right)}{m_e}.\end{array}$

Here,$v$is the speed ofan electron in the beam,$位$ is the wavelength with the value$0.062nm,$$p_{photon}$is the momentum of the photon,$m_e$is the mass of an electron, whose value is$9.1脳{10}^{鈭�31}\text{鈥塳驳}$, $h$ is the Plank鈥檚 constant whose value is$6.63脳{10}^{鈭�34}\text{鈥塉}鈰�\text{s}$.

Replaceall the known values in the above equation.

$\begin{array}{c}v=\frac{\left(\frac{6.63脳{10}^{鈭�34}\text{鈥塉}鈰�\text{s}}{0.062\text{鈥塶尘}脳\frac{{10}^{鈭�9}\text{鈥尘}}{1\text{鈥塶尘}}}\right)}{(9.1脳{10}^{鈭�31}\text{鈥塳驳})}\\ =1.18脳{10}^7\text{鈥�}J鈰�s/m鈰�kg\\ =(1.18脳{10}^7\text{鈥�}J鈰�s/m鈰�kg)脳\left(\frac{1m/s}{1J鈰�s/m鈰�kg}\right)\\ =1.18脳{10}^7\text{鈥�}m/s.\end{array}$

Thus, the speed ofelectron in the beamis$1.18脳{10}^7\text{鈥�}m/s.$