Question 6.12:
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).
Solution:
Electron is faster; Ratio of speeds is 13.54 : 1
Mass
of the electron, me
= 9.11 × 10–31
kgElectron is faster; Ratio of speeds is 13.54 : 1
Mass of the proton, mp = 1.67 × 10– 27 kg
Kinetic energy of the electron, EKe = 10 keV = 104 eV
= 104 × 1.60 × 10–19
= 1.60 × 10–15 J
Kinetic energy of the proton, EKp = 100 keV = 105 eV = 1.60 × 10–14 J
For the velocity of an electron ve, its kinetic energy is given by the relation:
EKe = (1/2) mve2
∴ ve = (2EKe / m)1/2
= (2 X 1.60 X 10-15 / 9.11 X 10-31)1/2 = 5.93 X 107 m/s
For the velocity of a proton vp, its kinetic energy is given by the relation:
EKp = (1/2)mvp2
vp = (2 X 1.6 X 10-14 / 1.67 X 10-27 )1/2 = 4.38 X 106 m/s
Hence, the electron is moving faster than the proton.
The ratio of their speeds
ve / vp = 5.93 X 107 / 4.38 X 106 = 13.54 / 1
No comments:
Post a Comment