QUANTUM PHYSICS FUNDAMENTALS - Chapter 1, Exercise 2 Solution
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Finding Frequency from Photon Energy

PROBLEM
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A photon has an energy of 4.14 x 10^-19 J. Using E = hf, calculate
its frequency.

SOLUTION
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Starting from Planck's relation:

    E = h f

Rearranged to solve for frequency:

    f = E / h

Substitute the given values:

    E = 4.14 x 10^-19 J
    h = 6.626 x 10^-34 J.s

    f = (4.14 x 10^-19) / (6.626 x 10^-34)
    f = 6.25 x 10^14 Hz (approximately)

ANSWER: The photon's frequency is approximately 6.25 x 10^14 Hz.

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WHY THIS WORKS AS AN ANSWER

Since E = hf is a simple direct proportionality with h as a fixed
constant, dividing the given energy by h directly recovers the
frequency - the same rearrangement technique used throughout this
course whenever two of the three quantities in a proportional
relationship are known. This particular frequency, 6.25 x 10^14 Hz,
falls within the real visible light spectrum (toward the blue/violet
end), consistent with the chapter's own examples of green and red
light sitting at somewhat lower frequencies.