In what region of the electromagnetic spectrum is a photon found that possesses twice as much energy as one in the blue region (442 nm) of the visible spectrum?

The answer is: ultraviolet The energy (E) of a photon is directly proportional to its frequency f, by Planck's formula: E = hf, where h is Planck's constant (6.625 * 10**-34 joule-second). The frequency is inversely proportional to the wavelength w by: f = c/w, where c is the speed of light, 3.0 * 10**8 meters per second. Combine these formulas and we see that the energy is inversely proportional to the wavelength by: E = hc/w If the energy is inversely proportional to the wavelength, a photon with twice the energy has half the wavelength of our 442-nm. photon in this example. So its wavelength is 221 nm. which is in the ultraviolet range.

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