A-level Physics (Advancing Physics)/Light as a Quantum Phenomenon/Worked Solutions

1. How much energy does a photon with a frequency of 50 kHz carry?

$E=hf=6.626\times 50\times 10^3\times 10^{-34}=3.313\times 10^{-29}\text{J}$

2. A photon carries 10⁻³⁰J of energy. What is its frequency?

$f=\frac{E}{h}=\frac{10^{-30}}{6.626\times 10^{-34}}\approx 1509\text{Hz}$

3. How many photons of frequency 545 THz does a 20W monochromatic bulb give out each second?

First calculate the amount of energy given out per. second:

$P=\frac{\mathrm{\Delta }E}{t}$

$\mathrm{\Delta }E=Pt=20\times 1=20\text{J}$

Then, calculate the amount of energy carried by each photon:

$E=hf=6.626\times 545\times 10^{12}\times 10^{-34}\approx 3.61\times 10^{-19}\text{J}$

Then divide the former by the latter to give the number of photons n:

$n=\frac{20}{3.61\times 10^{-19}}\approx 5.54\times 10^{19}\text{ photons}$

4. In one minute, a monochromatic bulb gives out a million photons of frequency 600 THz. What is the power of the bulb?

First calculate the energy carried by one photon:

$E=hf=6.626\times 10^{-34}\times 600\times 10^{12}\approx 3.98\times 10^{-19}\text{J}$

Then work out the energy carried by 1,000,000 photons:

$E=10^6\times 3.98\times 10^{-19}=3.98\times 10^{-13}\text{J}$

Then work out the power of the bulb:

$P=\frac{\mathrm{\Delta }E}{t}=\frac{3.98\times 10^{-13}}{60}=6.63\times 10^{-15}\text{W}$

...maybe its a nanobulb.

5. The photons in a beam of electromagnetic radiation carry 2.5μJ of energy each. How long should the phasors representing this radiation take to rotate?

First calculate the frequency of each photon:

$f=\frac{E}{h}=\frac{2.5\times 10^{-6}}{6.626\times 10^{-34}}\approx 3.77\times 10^{27}\text{Hz}$ (That's one nasty gamma ray.)

Then calculate the time taken for one 'wavelength' to go by:

$f=\frac{1}{t}$

$t=\frac{1}{f}=\frac{1}{3.77\times 10^{27}}\approx 2.65\times 10^{-28}\text{s}$