How to Calculate the Speed of an Electron

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Electrons are one of the three basic constituents of atoms, the other two being protons and neutrons. Electrons are extremely small even by the standards of subatomic particles, with each having a mass of 9 × 10-31 kg.

Because electrons carry a net charge, the value of which is 1.6 × 10-19coulombs (C), they are accelerated in an electromagnetic field in a manner analogous to the way ordinary particles are accelerated by a gravitational field or other external force. If you know the value of this field's potential difference, you can calculate the speed (or velocity) of an electron moving under its influence.

Step 1: Identify the Equation of Interest

You may recall that in everyday physics, the kinetic energy of an object in motion is equal to (0.5)mv2, where m equals mass and v equals velocity. The corresponding equation in electromagnetics is:

qV=0.5mv^2

where m = 9 × 10-31 kg and q, the charge of a single electron, is 1.6 × 10-19 C.

Step 2: Determine the Potential Difference Across the Field

You may have come to regard voltage as something pertaining to a motor or a battery. But in physics, voltage is a potential difference between different points in space within an electric field. Just as a ball rolls downhill or is carried downstream by a flowing river, an electron, being negatively charged, moves toward areas in the field that are positively charge, such as an anode.

Step 3: Solve for the Speed of the Electron

With the value of V in hand, you can rearrange the equation

qV=0.5mv^2

to

v=\sqrt{\frac{2qV}{m}}

For example, given V = 100 and the constants above, the speed of an electron in this field is:

v=\sqrt{\frac{2\times 1.6\times 10^{-19}\times 100}{9\times 10^{-31}}}=6\times 10^6\text{ m/s}

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