29.3 Photon Energies and the Electromagnetic Spectrum

A microwave oven produces electromagnetic radiation in the radio portion of the spectrum. These microwave photons are absorbed by water molecules, resulting in an increase in the molecules’ rotational energies. This added energy is transferred by heat to the surrounding food, which as a result becomes hot very quickly. If the energy absorbed by a water molecule is 1.0 × 10^–5 eV, what is the corres…

What is the energy in joules and eV of a photon in a radio wave from an AM station that has a 1530-kHz broadcast frequency?

Calculate the frequency in hertz of a 1.00-MeV $\gamma$-ray photon.

Do the unit conversions necessary to show that $\text{hc} = \text{1240 eV} \cdot \text{nm},$ as stated in the text.

(a) Calculate the energy in eV of an IR photon of frequency $\text{2}.\text{00} \times \text{10}^{\text{13}} \text{ Hz}.$ (b) How many of these photons would need to be absorbed simultaneously by a tightly bound molecule to break it apart? (c) What is the energy in eV of a $\gamma$ ray of frequency $3 . \text{00} \times \text{10}^{\text{20}} \text{ Hz}?$ (d) How many tightly bound molecules could a single such $\gamma$ ray break apart?

(a) What is the maximum energy in eV of photons produced in a CRT using a 25.0-kV accelerating potential, such as a color TV? (b) What is their frequency?

(a) What is the ratio of power outputs by two microwave ovens having frequencies of 950 and 2560 MHz, if they emit the same number of photons per second? (b) What is the ratio of photons per second if they have the same power output?

Some satellites use nuclear power. (a) If such a satellite emits a 1.00-W flux of $\gamma$ rays having an average energy of 0.500 MeV, how many are emitted per second? (b) These $\gamma$ rays affect other satellites. How far away must another satellite be to only receive one $\gamma$ ray per second per square meter?

How many x-ray photons per second are created by an x-ray tube that produces a flux of x rays having a power of 1.00 W? Assume the average energy per photon is 75.0 keV.

Assuming that 10.0% of a 100-W light bulb’s energy output is in the visible range (typical for incandescent bulbs) with an average wavelength of 580 nm, and that the photons spread out uniformly and are not absorbed by the atmosphere, how far away would you be if 500 photons per second enter the 3.00-mm diameter pupil of your eye? (This number easily stimulates the retina.)