Inspired By A JEE 2014 Question

The radiation corresponding to the \(2\rightarrow 1\) transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter an electric field of \(10^{-5} \text{ N/C}\) as shown in the figure. If the electrons just change their direction of motion after 1 second, then the work function of the metal is close to which of the following choices?

Details and Assumptions:

• Take the mass of electron, \(m_{e}=9.1\times 10^{-31}\text{ kg}\),

• The charge on electron, \(e=-1.6\times 10^{-19}\text{ C}\) and \(1\text{ eV}=1.6\times 10^{-19}\text{ J}\).

• The Ionization energy of Hydrogen atom in ground state is \(13.6 eV\)