A monochromatic beam of photons of intensity to 1.5 Wm⁻² and energy 11.2 eV is incident on a material of work function 4.8 eV. What is the maximum speed of photoelectrons emitted due to photoelectric effect if, only 0.53% of the incident photons eject photoelectrons. Given mass of electron m = 9 10⁻³¹ kg.

Step-by-step solution

Using Einstein's photoelectric equation: K_ = E - Substituting the given values for the energy of the incident photon and the work function: K_ = 11.2 eV - 4.8 eV = 6.4 eV Converting the maximum kinetic energy into Joules: K_ = 6.4 1.6 10⁻¹⁹ J = 10.24 10⁻¹⁹ J The maximum kinetic energy is related to the maximum speed by K_ = 1 2 m v_ ^2 . v_ = 2 K_ m Substituting the mass of the electron m = 9 10⁻³¹ kg : v_ = 2 10.24 10⁻¹⁹ 9 10⁻³¹ v_ = 20.48 10¹² 9 v_ = 4.525 3 10^6 1.5 10^6 m s ⁻¹ Answer: 1.5 10^6 ms⁻¹