Answer:
v = 5.9 x 10⁷ m/s
Explanation:
The kinetic energy of the electron in terms of potential difference is given as:
[tex]K.E = eV[/tex]--------------- equation (1)
where,
e = charge on electron = 1.6 x 10⁻¹⁹ C
V = Potential Difference = 9.9 KV = 9900 Volts
The kinetic energy in general is given as:
[tex]K.E = \frac{1}{2}mv^{2}\\[/tex]--------- equation (2)
where,
m = mass of electron = 9.1 x 10⁻³¹ kg
v = speed of electron = ?
Therefore, comparing equation (1) and equation (2), we get:
[tex]\\\frac{1}{2}mv^{2} = eV\\\\\frac{1}{2}(9.1\ x\ 10^{-31}\ kg)v^{2} = (1.6\ x\ 10^{-19}\ C)(9900\ volts)\\\\v = \sqrt{34.81\ x\ 10^{14}} \\[/tex]
v = 5.9 x 10⁷ m/s
