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skyluke89
The energy of a photon is given by
[tex]E=hf[/tex]
where h is the Planck constant and f is the frequency of the light. 
Given the relationship between the frequency f, the wavelength [tex]\lambda[/tex] and the speed of light c for an electromagnetic wave:
[tex]f= \frac{c}{\lambda} [/tex]
we can rewrite the energy of the photon as
[tex]\lambda = \frac{hc}{E} [/tex]
and by substituting [tex]h=6.6 \cdot 10^{-34 J}[/tex], [tex]c=3 \cdot 10^8 m/s[/tex] and [tex]E=2.87 \cdot 10^{-18}J[/tex], we get the wavelength of the photon:
[tex]\lambda = \frac{hc}{E}=6.9 \cdot 10^{-8} m = 69 nm [/tex]
samueladesida43

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;

  1. E = energy of the photon in Joules
  2. h = Planck's constant (6.623 × 10-³⁴ J/s)
  3. c = speed of light (3 × 10⁸m/s)
  4. λ = wavelength

  • According 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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