Question

In The Lord of the Rings: The Fellowship of the Ring, there is a scene in which Gandalf fights a Balrog, a sort of giant fire demon. The Balrog burns a bright red, giving off light with wavelengths of 650 ?? and 680 ??. The Balrog also puts out a lot of heat, with wavelengths of 1000 ?? and 1250 ??. For the sake of this question, we’ll say the Balrog emits these photons in equal quantities. The Balrog puts out a lot of heat. A typical bonfire gives off about 10 000 ? of energy per second, and this Balrog is worth at least four bonfires. Let’s say the Balrog gives off 40 000 ? of energy per second.

a. If these are the only four wavelengths of photons put out by the Balrog, find the number of photons it emits per second.

b. If these four photon energies were combined into a single photon, what would be the wavelength of that photon?

Answer 1

A) using E = n h c/

40000 = n * 6.63*3*10^(-26) { }

2.01 * 10^28 = n * (10^9) {1/650 + 1/680 + 1/1000 + 1/1250}

n = 4.18 * 10^ 21 photons per second of each type of wavelength.

Therefore, total number of photons emitted per second = 4 * 4.18 * 10^ 21 = 1.672 * 10 ^22

B) using , E = nhc/

40000 =1.672 * 10 ^22 * 6.63*3*10^(-26)/

= 83.14 nm

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