Final answer:
No photoelectrons will be emitted by the sphere before emission of photoelectrons stop.
Step-by-step explanation:
The maximum kinetic energy of a photoelectron at the metal surface is the difference between the energy of the incident photon and the work function of the metal. The work function is the binding energy of electrons to the metal surface. In this case, the energy of the incident photon is 4.2 eV and the work function is 1.5 eV.
Therefore, the maximum kinetic energy of the ejected photoelectrons is 4.2 eV - 1.5 eV = 2.7 eV.
To calculate the number of photoelectrons emitted before emission stops, we need to divide the total energy of the incident photons by the energy of each photoelectron. The energy of each photoelectron is the maximum kinetic energy calculated earlier.
Let's assume N represents the number of photoelectrons emitted. The total energy of the incident photons is N * 4.2 eV. Setting this equal to the energy of each photoelectron times the number of photoelectrons, we have:
N * 4.2 eV = N * 2.7 eV
Simplifying the equation, we find:
1.5 N = 0
Since the coefficient of N is 1.5 and it equals zero, N must be zero. This means that no photoelectrons will be emitted by the sphere before emission of photoelectrons stop.