The velocity of an electron so that its momentum is equal to that of a photon of wavelength 660 ~nm is

Step-by-step solution

The momentum of a photon is given by p = h . Given = 660 nm = 660 10⁻⁹ m . The momentum of an electron is p = mv . Equating the two: mv = h v = h m Substituting the values h = 6.626 10⁻³⁴ J s , m = 9.1 imes 10⁻³¹ kg , and = 660 10⁻⁹ m : v = 6.626 10⁻³⁴ (9.1 10⁻³¹) (660 10⁻⁹) v = 6.626 10⁻³⁴ 6006 10⁻⁴⁰ v = 6.626 6006 10⁶ m s ⁻¹ v 0.001103 10⁶ m s ⁻¹ = 1103 m s ⁻¹ . Using h = 6.6 10⁻³⁴ J s for approximation: v = 6.6 10⁻³⁴ 9.1 10⁻³¹ 660 10⁻⁹ = 6.6 10⁻³⁴ 6006 10⁻⁴⁰ = 6.6 6006 10⁶ 1098.9 m s ⁻¹ . This value is approxima