A beam of monochromatic light of wavelength is used to eject photoelectrons from a cesium surface ( = 1.9 eV ). The ejected photoelectrons are then made to collide with ground-state hydrogen atoms. Find the maximum value of for which the hydrogen atoms may get excited from the ground state to the first excited state.

Step-by-step solution

The energy required to excite a hydrogen atom from the ground state ( n=1 ) to the first excited state ( n=2 ) is given by: E = 13.6 ( 1 1^2 - 1 2^2 ) eV = 10.2 eV For the ejected photoelectrons to excite the hydrogen atoms, their maximum kinetic energy must be at least equal to this excitation energy. To find the maximum wavelength of the incident light, we consider the case where the maximum kinetic energy of the photoelectrons is exactly 10.2 eV . Using Einstein's photoelectric equation: K_ max = hc - Substituti