Question

A photon of 300 nm is absorbed by a gas and then re-emits two photons. One re-emitted photon has a wavelength of 496 nm. The wavelength of the second re-emitted photon is:

a) 248 nm
b) 372 nm
c) 496 nm
d) 744 nm

Answer 1

Using the conservation of energy for the re-emission of photons, the wavelength of the second re-emitted photon, when one of the re-emitted photons has a wavelength of 496 nm, is determined to be 744 nm (option d).

Step-by-step explanation:

The subject of the question is regarding the re-emission of photons by a gas after the absorption of a photon. This is a concept typically covered in high school physics, particularly when discussing the conservation of energy and properties of photons.

To determine the wavelength of the second re-emitted photon, we can use the conservation of energy. The energy of a photon is inversely proportional to its wavelength, as shown by the equation E = hc/λ, where E is the energy, h is Planck's constant, and λ is the wavelength of the photon. Knowing this relationship, when one photon is absorbed and two are emitted, the sum of the energies of the two emitted photons must equal the energy of the absorbed photon.

We can calculate the energy of the absorbed photon with a wavelength of 300 nm and set it equal to the sum of the energies of the two re-emitted photons, with one having a wavelength of 496 nm. Using this method, we can find the wavelength of the second photon. The equation we use is Eabsorbed = Eemitted1 + Eemitted2 or (hc/300 nm) = (hc/496 nm) + (hc/λemitted2). Cancelling out the common factor of hc gives 1/300 nm = 1/496 nm + 1/λemitted2. Solving for λemitted2 gives us the wavelength of the second photon, which is option (d) 744 nm.