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

first, consult an activity series chart to determine if al is more reactive than fe. it is, so it will replace the fe. now, one can continue with the problem.

next, make sure you have a correctly balanced equation.

3feo + 2al ==> 3fe + al2o3

now, determine which reactant (feo or al) is in limiting supply.

moles feo present = 125 g x 1 mole/71.8 g = 1.74 moles

moles al present = 25.0 g x 1 mole/26.98 g = 0.927 moles

since from the balanced equation, it take 3 mol feo for every 2 mol al, al will be limiting.

you can determine this simply by dividing moles of each by their coefficient in the balanced equation. for example: 1.74/3 = 0.58 and 0.927/2 = 0.464. al is less, so it is limiting.

finally, using the stoichiometry in the balanced eq. determine mass of fe that can be produced from 0.927 moles of al.

0.927 moles al x 3 moles fe/2 moles al x 55.8 g/mole = 77.6 g