Concept: The relationship between the energy of a photon and its wavelength is governed by Planck's equation, showing an inverse proportionality.
Formula: $$ E = \frac{hc}{\lambda} $$
Solution: - In the equation, \( E \) is energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is wavelength.
- Because \( \lambda \) is in the denominator, as wavelength increases (gets greater), the total energy of the photon decreases (gets smaller).
- Long-wavelength radiation (like radio waves) has very low energy, while short-wavelength radiation (like gamma rays) has massive energy.
Why other options are incorrect: Energy is not directly proportional, nor is it independent (constant or random variable) with respect to wavelength.
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