Question

Why is the transverse spatial extent of a photon proportional to its wavelength which is a longitudinal quantity?

Answer 1

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In quantum mechanics, the uncertainty principle also known as "Heisenberg's uncertainty principle" is any of a variety of mathematical inequalities, asserting a fundamental limit to the precision with certain pairs of physical properties of a particle known as complimentary variables, such as position X and momentum P can be known.

Answer 2

In quantum mechanics, particularly the wave-particle theory, it states that light behaves like a wave or a particle. For the wave behavior, its movement is measured in wavelengths while the time for each wavelength is the frequency. For the particle behavior, according to Planck, the energy of the photon (light particle) is determined as

E = hc/wavelength, where h is the Planck's constant (6.626 x 10-34 J-s per particle) and c is the speed of light ( 3 x 10^8m/s)

As you can see, the energy of the photon is INVERSELY PROPORTIONAL to the wavelength with the Planck's constant as the constant of proportionality.