Find the velocity of an electron when its kinetic energy is equal to one electron volt (in 10 5 m/s). Given charge of an electron e = 1.6 x 10 -19 and mass of an electron m = 9.1 x 10

To find the velocity of an electron when its kinetic energy (K) is equal to 1 electron volt (eV), we use the relation between kinetic energy and velocity, and the given values for the charge (e) and mass (m) of an electron.

The kinetic energy K in joules for an electron can be given by the equation ( K = frac{1}{2} mv^2 ), where (m) is the mass of the electron and (v) is its velocity.

Given:

– (K = 1 , text{eV} = 1.6 times 10^{-19} , text{J}) (since (1 , text{eV} = 1.6 times 10^{-19} , text{J}))

– (m = 9.1 times 10^{-31} , text{kg})

– (e = 1.6 times 10^{-19} , text{C}) (charge of the electron, although it’s not directly used in the calculation for velocity, it’s useful for understanding the energy conversion)

Starting with the relationship between kinetic energy and velocity:

[ K = frac{1}{2} mv^2 ]

Solving for (v):

[ v = sqrt{frac{2K}{m}} ]

Plugging in the values:

[ v =