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)

Step-by-step solution

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