Work, Energy and Power NCERT Solutions Class 11 Physics - Solved Exercise Question 6.12

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, m_e = 9.11 × 10^–31 kg
Mass of the proton, m_p = 1.67 × 10^{– 27} kg
Kinetic energy of the electron, E_Ke = 10 keV = 10⁴ eV
= 10⁴ × 1.60 × 10^–19
= 1.60 × 10^–15 J
Kinetic energy of the proton, E_Kp = 100 keV = 10⁵ eV = 1.60 × 10^–14 J
For the velocity of an electron v_e, its kinetic energy is given by the relation:
E_Ke = (1/2) mv_e²
∴ v_e = (2E_Ke / 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 v_p, its kinetic energy is given by the relation:
E_Kp = (1/2)mv_p²
v_p = (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
v_e / v_p = 5.93 X 10⁷ / 4.38 X 10⁶  =  13.54 / 1