4. An electron and a proton are detected in a cosmic ray experiment, the electron with K.E. of 5 keV and the proton with K.E. of 50 keV. Find the ratio of their speeds. Given m = 9.11 x 10 m, = 9.11 x 10 31 kg and , 1.67 x 10 kg Ans. 27 Ve = 4.28
Answers
Answer:
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Explanation:
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Answer:
Solution
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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