ELECTROMAGNETISM & RELATIVITY - Chapter 9, Exercise 2 Solution
==========================================================
Photon Energy from Momentum (E = pc)

PROBLEM
-------
A photon has momentum p = 2 x 10^-27 kg.m/s and zero rest mass. Using
E = pc, calculate its energy.

SOLUTION
--------
Using the massless-particle form of the energy-momentum relation:

    E = p c

Substitute the given values:

    p = 2 x 10^-27 kg.m/s
    c = 3 x 10^8 m/s

    E = (2 x 10^-27) x (3 x 10^8)
    E = 6 x 10^-19 J

ANSWER: The photon's energy is 6 x 10^-19 J.

----
WHY THIS WORKS AS AN ANSWER

Since the photon has zero rest mass (m = 0), the general relation
E^2 = (pc)^2 + (mc^2)^2 simplifies directly to E = pc, with the
entire (mc^2)^2 term dropping out completely - a genuinely different
simplification from the E = mc^2 case used in Exercise 1, which
instead relies on p = 0 (an object at rest). This result, 6 x 10^-19
J, is a physically realistic scale for a single visible-light photon
(roughly equivalent to a few electron-volts) - demonstrating that
even though a photon carries no rest mass at all, it still carries
real, measurable energy and momentum, exactly as the chapter's own
text states.