# Speed and Mass Ratios

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Calculate the ratio of v/c and m/m_o for

a) 100 keV electron

b) 1 MeV electron

c) 1 MeV proton

d) 100 MeV proton

Note: m_o is rest mass

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#### Solution Preview

m= mo/square root of (1-v^2/c^2)

or m/ mo= 1/square root of (1-v^2/c^2)

But (1/square root of (1-v^2/c^2)= 1+T/(moc^2)=

where T is the kinetic energy

Therefore

m/ mo=1+T/(moc^2)

Also by similar manipulation of the terms v/c= square root of {1- (mo/m)^2}

a) 100 keV electron

mo= rest mass = 9.1E-31 Kg

c= speed of light = ...

#### Solution Summary

This solution calculates speed ratios (speed / speed of light ) and mass ratios (mass / mass at rest ) of electrons and protons.

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