QUANTUM PHYSICS FUNDAMENTALS - Chapter 2, Exercise 1 Solution
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Maximum Kinetic Energy of Ejected Electrons

PROBLEM
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Light with a frequency of 6 x 10^14 Hz strikes a metal with a work
function of 2.5 x 10^-19 J. Calculate the maximum kinetic energy of
the ejected electrons.

SOLUTION
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Using Einstein's photoelectric equation:

    KE_max = h f - W

Substitute the given values:

    h = 6.626 x 10^-34 J.s
    f = 6 x 10^14 Hz
    W = 2.5 x 10^-19 J

    KE_max = (6.626 x 10^-34 x 6 x 10^14) - (2.5 x 10^-19)
    KE_max = (3.9756 x 10^-19) - (2.5 x 10^-19)
    KE_max = 1.48 x 10^-19 J (approximately)

ANSWER: The maximum kinetic energy of the ejected electrons is
approximately 1.48 x 10^-19 J.

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WHY THIS WORKS AS AN ANSWER

The photon's own total energy (hf) is fixed by its frequency alone,
regardless of how many photons (how bright the light) arrive. Once a
photon is absorbed, a fixed portion of its energy (W, the work
function) must be spent freeing the electron from the metal's own
surface - whatever energy remains becomes the electron's real,
measurable kinetic energy. This is exactly why intensity never
enters this calculation at all: each individual photon-electron
interaction is an independent, one-at-a-time event, not something
that accumulates energy from multiple photons over time.