When radiations of wavelength `lambda_(1), lambda_(2) (= 0.6 lambda_(1)), lambda_(3) (= 4lambda_(2))` and `lambda_(4)` are incident on a metal plate, photoelectrons with maximum kinetic energy of – 5.2 eV are emitted for `lambda_(1), 12 eV` are emitted for `lambda_(2), 0.95 eV` are emitted for `lambda_(4)` and no electron is emitted for l3. It is known that a hydrogen like atom (atomic number Z) in a higher excited state of quantum number n can make a transition to first excited state by successively emitting two photons of wavelength `lambda1` and `lambda_(2)` respectively. Alternatively, the atom from same excited state can make a transition to the second excited state by successively emitting two photons of wavelength `lambda_(3)` and `lambda_(4)` respectively.
(a) Find the work function of the metal.
(b) Find the values of n and Z for the atom.

Answer

(a) `5 eV` , (b) `n = 6, Z = 3`