When a light beam of frequency is incident on a metal surface, photoelectrons are emitted. If these electrons describe a circle of radius r in a magnetic field of strength B, then the work function of the metal is (h = Planck's constant, m_e = mass of electron, e = charge on electron )

Step-by-step solution

Using Einstein's photoelectric equation: K_ = h - W When an electron moves in a circular path in a uniform magnetic field, the necessary centripetal force is provided by the magnetic force: m_e v^2 r = e v B v = e B r m_e The maximum kinetic energy of the photoelectron is: K_ = 1 2 m_e v^2 = 1 2 m_e ( e B r m_e )^2 = (B e r)^2 2 m_e Substituting K_ into the photoelectric equation: (B e r)^2 2 m_e = h - W W = h - (B e r)^2 2 m_e Answer: h - (Ber)^2 2m_e