The path of photoelectrons emitted due to electromagnetic radiation incident on a sample of material A, is found to have a maximum bending radius of 0.1 m in a magnetic field of `((sqrt2)/(3))xx10^-4`T. When the radiation is incident normally on a double slit having a slit separation of 0.1mm, it is observed that there are 10 fringes in a width of 3.1 cm on a screen placed at a distance of 1 m from the double slit. Find the work function of the material. and the corresponding threshold wavelength. What sould be the wavelength of the incident light so that the bending radius is one-half of what it was before? Given that mass of the electron`=0.5Me(V)/(c^2)`,`hc=12400eV-A`

Explanation

To solve the problem step by step, we will break it down into manageable parts:

### Step 1: Calculate the Kinetic Energy of the Photoelectrons

The bending radius \( R \) of the photoelectrons in a magnetic field is given by the formula:

\[
R = \frac{mv}{qB}
...