Find the mass and speed of 2MeV electron (use relativistic mechanics).

To find the mass and speed of a 2MeV electron using relativistic mechanics, we can use the equation:

E = γmc^2

where E is the energy of the electron, m is its mass, c is the speed of light, and γ is the Lorentz factor given by:

γ = 1 / sqrt(1 - (v^2 / c^2))

where v is the velocity of the electron.

Given that the energy of the electron is 2MeV, we can convert it to joules by using the conversion factor 1MeV = 1.6 x 10^-13 J. Therefore, the energy of the electron is:

E = 2MeV * (1.6 x 10^-13 J/MeV) = 3.2 x 10^-13 J

Now, we can rearrange the equation to solve for the mass:

m = E / (γc^2)

To find the Lorentz factor γ, we need to solve for the velocity v. Rearranging the equation, we have:

v = c * sqrt(1 - (1 / γ^2))

Now, let's substitute the values into the equations:

E = 3.2 x 10^-13 J c = 3 x 10^8 m/s

First, we need to find γ:

γ = 1 / sqrt(1 - (v^2 / c^2))

Next, we can solve for v:

v = c * sqrt(1 - (1 / γ^2))

Finally, we can substitute the values into the equations to find the mass and speed of the electron.