What wavelength of radiation has photons of energy 2.87×x10−18 j?

The wavelength of radiation that has a photon of energy of 2.87 × 10-¹⁸J is 7.2 × 10-⁸nm

HOW TO CALCULATE WAVELENGTH:

The wavelength of a wave can be calculated by using the formula as follows:

E = hc/λ

Where;

E = energy of the photon in Joulesh = Planck's constant (6.623 × 10-³⁴ J/s)c = speed of light (3 × 10⁸m/s)λ = wavelengthAccording to this question, a wavelength of radiation has photons of energy 2.87 x 10-¹⁸J. The energy can be calculated as follows:

λ = (6.626 × 10-³⁴ × 3 × 10⁸) ÷ 2.87 × 10-¹⁸

λ = 19.88 × 10-²⁶ ÷ 2.78 × 10-¹⁸

λ = 7.2 × 10-²⁶+¹⁸

λ = 7.2 × 10-⁸nm

Therefore, the wavelength of radiation that has a photon of energy of 2.87 × 10-¹⁸J is 7.2 × 10-⁸nm.

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The energy of a photon is given by

where h is the Planck constant and f is the frequency of the light. 
Given the relationship between the frequency f, the wavelength  and the speed of light c for an electromagnetic wave:

we can rewrite the energy of the photon as

and by substituting ,  and , we get the wavelength of the photon: