Photoelectric Effect

The slopes and represent the Planck constant divided by the charge in the photoelectric equation . Since the slopes depend on universal constants and , they are the same for any material, leading to a ratio .

Step 1: Use Einstein's photoelectric equation
The maximum kinetic energy ( ) of the emitted photoelectrons is given by: where: - is the energy of the incident photon, - is the work function of the metal.

Step 2: Compute the kinetic energy for each incident photon
For eV: For eV:

Step 3: Compute the ratio of maximum velocities
The maximum velocity ( ) of the emitted photoelectrons is related to the kinetic energy by: Thus, the ratio of maximum velocities is: Thus, the required ratio is . \

Step 1: Understanding the Concept of Conservation of Momentum Since the parent nucleus was initially at rest, the total momentum of the daughter nuclei must be equal and opposite due to conservation of linear momentum: where:
- (mass number of nucleus ),
- (mass number of nucleus ),
- and are their respective velocities.

Step 2: Kinetic Energy Relation Kinetic energy is given by: Dividing the kinetic energies of the two nuclei: Since , we can express velocity as: Substituting into the energy equation: Thus, the correct answer is .