Answer :
Final answer:
The momentum of the proton in the presented scenario would be P = sqrt(6) m_proton * c. The work function of the metal is found by the equation phi = hf - KE_max, which is a principle derived from the photoelectric effect where the energy of an incident photon is equal to the work function of the material minus maximum kinetic energy of ejected electrons.
Explanation:
The proton has a kinetic energy that is three times its rest mass energy which is given as K = 3mc^2. Please note that c is the speed of light. However, the relativistic momentum P of an object with mass m and kinetic energy K is given by P = sqrt(2mK). So, substituting for K, the momentum of the proton will be P = sqrt(2* m_proton * 3 * m_proton * c^2) = sqrt(6) m_proton * c.
In the second part of the question, the metal ejects electrons with maximum kinetic energy when hit by photons. This concept, known as the photoelectric effect, is based on the energy of the incoming photon being equal to the work function of the material (phi = hf - KE_max). The work function is thus given by phi = hf - KE_eject. Here, f is the frequency of the light which we can find from the given wavelength λ using the relation f = c/λ. Here, h is Planck's constant, and KE_eject is the kinetic energy of the ejected electron.
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