Scientists are studying ways to improve the efficiency of solar cells by studying a process called photon upconversion . In this process , the energy of two photons can become combined to form a new photon with an energy equal to the sum of the two combined photons . With this process , abundant infrared radiation can be converted into visible light that can be used by solar celis to produce electricity . Suppose an infrared photon with a wavelength of 853 nm were combined with another infrared photon with a wavelength of 935 nm , what would be the wavelength of the new 'combined photon , in nm ?

λ = 4.46 x 10⁻⁷ m = 446 nm

Explanation:

Applying Law of Conservation of Energy in this condition, we will get the following equation:

Total Energy of Combined Photons = Energy of 1st Photon + Energy of 2nd Photon

hc/λ = hc/λ₁ + hc/λ₂

hc/λ = hc(1/λ₁ + 1/λ₂)

1/λ = 1/λ₁ + 1/λ₂

where,

λ = wavelength of combined photon = ?

λ₁ = wavelength of 1st photon = 853 nm = 8.53 x 10⁻⁷ m

λ₂ = wavelength of 2nd photon = 935 nm = 9.35 x 10⁻⁷ m

Therefore,

1/λ = 1/(8.53 x 10⁻⁷ m) + (9.35 x 10⁻⁷ m)

1/λ = (0.1172 x 10⁷ m⁻¹) + (0.1069 x 10⁷ m)

1/λ = 0.2241 x 10⁷ m⁻¹

λ = 1/(0.2241 x 10⁷ m⁻¹)

λ = 4.46 x 10⁻⁷ m = 446 nm

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