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Answer:
Explanation:
Given the data in the question;
wavelength λ₁ = 853 nm = 853 × 10⁻⁹ m
wavelength λ₂ = 865 nm = 865 × 10⁻⁹ m
we determine the energy of each photons using the following expression;
[tex]E_{photon[/tex] = hc / λ
where h is Planck's constant ( 6.626 × 10⁻³⁴ J.s )
c is speed of light ( 3 × 10⁸ m/s )
For Photon with wavelength λ₁ = 853 × 10⁻⁹ m
[tex]E_{photon1[/tex] = hc / λ
we substitute
= ( ( 6.626 × 10⁻³⁴ J.s )( 3 × 10⁸ m/s ) ) / (853 × 10⁻⁹ m)
= 1.9878 × 10⁻²⁵ / 853 × 10⁻⁹
= 2.33 × 10⁻¹⁹ J
For Photon with wavelength λ₂ = 865 × 10⁻⁹ m
[tex]E_{photon2[/tex] = ( ( 6.626 × 10⁻³⁴ J.s )( 3 × 10⁸ m/s ) ) / (865 × 10⁻⁹ m)
= 1.9878 × 10⁻²⁵ / 865 × 10⁻⁹
= 2.298 × 10⁻¹⁹ J
We know that; energy of the combined photon will be equal to the sum of energies of the two photons.
so
Energy of the combined photon = [tex]E_{photon1[/tex] + [tex]E_{photon2[/tex]
[tex]E_{combined[/tex] = 2.33 × 10⁻¹⁹ J + 2.298 × 10⁻¹⁹ J
[tex]E_{combined[/tex] = 4.628 × 10⁻¹⁹ J
so wavelength of the new combined photon will be;
[tex]E_{combined[/tex] = hc / λ[tex]_{combined[/tex]
[tex]E_{combined[/tex]λ[tex]_{combined[/tex] = hc
λ[tex]_{combined[/tex] = hc / [tex]E_{combined[/tex]
we substitute
λ[tex]_{combined[/tex] = ( ( 6.626 × 10⁻³⁴ J.s )( 3 × 10⁸ m/s ) ) / 4.628 × 10⁻¹⁹ J
= 1.9878 × 10⁻²⁵ / 4.628 × 10⁻¹⁹
= 4.2952 × 10⁻⁷ m
= ( 4.2952 × 10⁻⁷ × 10⁹ )nm
= 429.5 nm
Therefore, Wavelength of the new 'combined' photon is 429.5 nm