# Calculating Speed of Electron after 50keV Work

• Brown Arrow
In summary, the problem is to find the initial speed of an electron that is initially at rest, given that a total work of 50 keV is done on it. We can convert the work to total energy and use the relativistic energy equation, taking into account the rest mass of the electron.
Brown Arrow

## Homework Statement

what is the speed of en electro, initially at rest,if a total work of 50keV is done on it?
1eV=1.6*10-19j me=9.11*10-31kg

## Homework Equations

relastic energy equaltion.

## The Attempt at a Solution

i converted the total work to total energy

Etotal=8*10-15

then i set Etotal=(mc2)/(1-(v/c)2)1/2
when i try solving it i keep getting sqrt of a negative #
could someone tell me where I am going wrong

You have to include the rest mass as part of the total energy, not just the work done on the particle

oh i see thanks!
let me see if it works

yeah it works thanks again !

Your attempt at a solution is on the right track, but there are a few mistakes. First, the formula you used is the relativistic energy equation for a particle at rest, not in motion. To calculate the speed of the electron after the work is done, you need to use the formula for kinetic energy:

K = (γ - 1)mc^2

where γ is the Lorentz factor:

γ = 1/√(1 - v^2/c^2)

Also, you need to use the rest mass of the electron, not the mass-energy equivalent. So your final equation should be:

K = (1/√(1 - v^2/c^2) - 1) * 9.11*10^-31 * c^2 = 50 * 1.6*10^-19

Solving for v, you get v = 0.9999999999999999 * c, which is essentially the speed of light. This makes sense because 50keV is a very high amount of energy, and the electron would be moving very close to the speed of light after that. Hope this helps!

## What is the formula for calculating the speed of an electron after 50keV work?

The formula is: v = √(2eV/m), where v is the speed of the electron, e is the electron's charge, V is the potential difference (in volts), and m is the mass of the electron.

## How do you convert 50keV into joules?

To convert from keV to joules, you can use the conversion factor 1 keV = 1.602 x 10^-16 joules. Therefore, 50 keV is equal to 8.01 x 10^-15 joules.

## What is the mass of an electron?

The mass of an electron is approximately 9.109 x 10^-31 kilograms.

## What is the potential difference required to accelerate an electron to a speed of 50% the speed of light?

To calculate the potential difference, we can rearrange the formula v = √(2eV/m) to solve for V. Plugging in the known values of v = 0.5c (where c is the speed of light) and m = 9.109 x 10^-31 kg, we get V = 5.62 x 10^6 volts. This is equivalent to 5.62 megavolts (MV).

## How does the speed of an electron change when the potential difference is doubled?

According to the formula v = √(2eV/m), the speed of the electron is directly proportional to the square root of the potential difference. This means that if the potential difference is doubled, the speed of the electron will also double.

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