Energy of the quantum
Task number: 4376
All electromagnetic radiation is mediated by photons which are characterized by wavelength, frequency, energy and momentum.
Calculate how big the quantum of energy is for the
- Signal from ČR1 Radiožurnál broadcasted from Prague on the frequency of 95 MHz,
- Wave from radio navigation to the southeast of the Ruzyně airport on the frequency of 127 MHz,
- Waves broadcasted/received by a mobile phone working on the frequency of 900 MHz,
- Waves broadcasted/received by a mobile phone working on the frequency of 1 800 MHz,
- Radiation in a microwave which has frequency of 2 450 MHz,
- Signal of satellite digital broadcasting channel ČT1 on the frequency of 12 382 MHz.
For all the cases determine the corresponding wavelength.
Notation
f1 = 95 MHz broadcasting frequency ČR1 Radiožurnál f2 = 127 MHz radio navigation frequency near Prague airport f3 = 900 MHz signal frequency from mobile phone f4 = 1 800 MHz signal frequency from mobile phone f5 = 2 450 MHz radiation frequency in microwave f6 = 12 382 MHz frequency of satellite digital broadcasting channel ČT1 λi = ? (m) wavelength of i-th radiation source Ei = ? (eV) energy of i-th radiation source
From tables:
h = 6.6·10−34 J s Planck’s constant in SI units h = 4.1·10−15 eV s Planck’s constant in eV s units c = 3.0·108 m s−1 speed of light Hint
Energy of a photon is proportionate to the frequency of the corresponding wavelength.
Wavelength is inversely proportional to the photon’s frequency.
You can read more about properties of photon here
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Solution
Photon has zero rest mass and moves with speed of light. Photon’s overall energy is proportional to the frequency f of given wavelength
\[E = hf ,\]where h is the Planck’s constant.
We can determine the corresponding wavelength of electromagnetic radiation with the following formula
\[\lambda = {c \over f},\]where c is the speed of light in vacuum.
Now we can easily determine the characteristics of given wavelengths:
f λ E 1. 95 MHz 3.16 m 0.4 μeV 2. 127 MHz 2.36 m 0.5 μeV 3. 900 MHz 0.33 m 3.7 μeV 4. 1 800 MHz 0.17 m 7.4 μeV 5. 2 450 MHz 0.12 m 10.1 μeV 6. 12 382 MHz 0.02 m 51.2 μeV Answer
Wavelength and quantum of energy for given frequencies are shown in the following table:
f λ E a. 95 MHz 3.16 m 0.4 μeV b. 127 MHz 2.36 m 0.5 μeV c. 900 MHz 0.33 m 3.7 μeV d. 1 800 MHz 0.17 m 7.4 μeV e. 2 450 MHz 0.12 m 10.1 μeV f. 12 382 MHz 0.02 m 51.2 μeV
