A quantum of electromagnetic radiation has an energy of 2.64 keV. What is its wavelength? The speed of light is 2.99792 × 108 m/s, and Planck’s constant is 6.62607 × 10−34 J · s. Answer in units of nm.

λ = 46.4 x 10^(-9) = 46.4 nm

Explanation:

We are given,

Energy; E = 2.64 keV = 2.64 x 1.602 x 10^(-16) J

The energy of a photon is proportional to its frequency, as stated by the Planck - Einstein's equation;

E = h•ν

where;

E is the energy of the photon

h is Planck's constant, equal to

6.626 x 10^(−34) J.s

ν is the frequency of the photon

Now, notice that we are given the speed of light and asked to find wavelength of the photon,

λ. Now, frequency and wavelength have an inverse relationship described by the equation;

λ⋅ν = c or ν = c/λ

where;

c is the speed of light in vacuum, approximately equal to 2.99792 × 10^(8) m/s

This means that the relationship between energy and wavelength looks like this;

E = h(c/λ)

Let's make the wavelength λ the subject;

Thus,

λ = hc/E

Plugging in the relevant values to obtain;

λ = [6.626 x 10^(−34) x 2.99792 × 10^(8)]/(2.64 x 1.602 x 10^(-16))

λ = 46.4 x 10^(-9) = 46.4 nm

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