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?

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

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

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

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:

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

$\Delta E=Pt=20\times 1=20{\mbox{J}}\,$

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

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

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

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

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:

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

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

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

Then work out the power of the bulb:

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

...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:

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

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

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

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