What is the energy of an electromagnetic wave that has a wavelength of 7.0×10^-12 m? Use the equation E- Intion hc

Assume that this wavelength is measured in vacuum. The energy on each photon of this wave would be approximately .

Explanation:

The Planck-Einstein Relation relates the energy of a photon to its frequency :

,

where is Planck's Constant.

.

This question did not provide the frequency of this wave directly; the value of needs to be calculated from the wavelength of this wave. Assume that this wave is travelling at the speed of light in vacuum:

.

The frequency of this electromagnetic wave would be:

.

Apply the Planck-Einstein Relation to find the energy of a photon of this electromagnetic wave:

.

Note that combining the two equations above ( and ) will give:

.

This equation is supposed to give the same result (energy of a photon of this wave given its wavelength and speed) in one step:

.

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