$$An electron in a cathode$-$ray beam passes between $2\mathrm{.}5-$cm$-$long parallel$-$plate electrodes that are $5\mathrm{.}0$ mm apart. A $1\mathrm{.}0$ mT$,2\mathrm{.}5-$cm wide magnetic field is perpendicular to the electric field between the plates. If the potential difference between the plates is $150$ V$,$ the electron passes through the electrodes without being deflected. If the potential difference across the plates is set to zero, through what angle is the electron deflected as it passes through the magnetic field?

$$

$$

$$

$$

$$

$$

b$.$ You need to design a detector that can respond to the entire range of visible light. What is the maximum possible work function of the cathode?

b$.$ Through what potential difference$$ must an electron be accelerated from rest to have a debBroglie wavelength of $500$ nm$?$