A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron p_e to that of photon p_ Ph , p_e p_ Ph is : (Take speed of light =3 10^8 ms^ -1 , charge of electron =-1.6 10^ -19 C and mass of electron =9 10^ -31 kg)
D. 225
For a photon, the energy E and linear momentum p_ Ph are related by: p_ Ph = E c For an electron, the kinetic energy E and linear momentum p_e are related by: p_e = 2mE The ratio of the linear momentum of the electron to that of the photon is: p_e p_ Ph = 2mE E c = c 2m E Given: E = 20 eV = 20 1.6 10^ -19 J = 32 10^ -19 J m = 9 10^ -31 kg c = 3 10^8 m/s Substituting the values into the ratio: p_e p_ Ph = 3 10^8 2 9 10^ -31 32 10^ -19 p_e p_ Ph = 3 10^8 18 10^ -31 32 10^ -19 p_e p_ Ph = 3 10^8 9 16 10^ -12 p_e p_ Ph = 3 10^8 ( 3 4 10^ -6 ) p_e p_ Ph = 9 4 10^2 = 2.25 100 = 225
Related: Physics — Dual Nature of Matter · All PYQ Banks