An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. Which is faster, the electron or the proton ? Obtain the ratio of their speeds. (electron mass = 9.11×10-31 kg, proton mass = 1.67×10–27 kg, 1 eV = 1.60 ×10–19 J).
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Mass of the electron, m
e
=9.11×10
−31
kg
Mass of the proton, m
p
=1.67×10
−27
kg
Kinetic energy of the electron is
E
e
=10keV=10
4
eV
E
e
=10
4
×1.6×10
−19
=1.60×10
−15
J
Kinetic energy of the proton
E
p
=100keV=10
5
eV=1.60×10
−14
J
For the velocity of an electron v
e
, its kinetic energy is given by the relation:
E
e
=
2
1
mv
e
2
⇒v
e
=
9.11×10
−31
2×1.6×10
−15
=5.93×10
7
m/s
For the velocity of a proton v
p
, its kinetic energy is given by the relation:
E
p
=
2
1
mv
p
2
v
p
=4.38×10
6
m/s
As the velocity of electron is more than that of proton, so electron is faster than proton.
The ratio of their speeds is
v
p
v
e
=
4.38×10
6
5.93×10
7
=
1
13.54
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