Question Video: Calculating the Momentum of a Photon Given Its Frequency | Nagwa Question Video: Calculating the Momentum of a Photon Given Its Frequency | Nagwa

Question Video: Calculating the Momentum of a Photon Given Its Frequency Physics • Third Year of Secondary School

A low-frequency radio wave has a frequency of 200 kHz. What is the momentum of a radio-wave photon with this frequency? Use a value of 6.63 × 10⁻³⁴ J⋅s for the Planck constant. Give your answer in scientific notation to two decimal places.

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Video Transcript

A low-frequency radio wave has a frequency of 200 kilohertz. What is the momentum of a radio-wave photon with this frequency? Use a value of 6.63 times 10 to the negative 34 joule-seconds for the Planck constant. Give your answer in scientific notation to two decimal places.

This question asks us to determine the momentum of a photon given its frequency. We can recall that the momentum of a photon is given by the formula 𝑝 is equal to ℎ times 𝑓 divided by 𝑐, where 𝑝 is the momentum of a photon, ℎ is the Planck constant, 𝑓 is the frequency of the photon, and 𝑐 is the speed of light in vacuum. We are given a value for the frequency and also value for the Planck constant. The only other value we need to use this formula is the speed of light in vacuum.

The question asks us to report our answer to two decimal places. For this kind of accuracy, it is sufficient to report the speed of light as 3.00 times 10 to the eighth meters per second. Combining this value with the values from the statement, we can write the momentum of our photon as 6.63 times 10 to the negative 34 joule- seconds times 200 kilohertz divided by 3.00 times 10 to the eighth meters per second.

Before we actually calculate this value, let’s pay attention to the units. We are calculating a momentum. And in basic SI units, the units for momentum are kilogram-meters per second. Our answer is guaranteed to have these correct units as long as the units of all of our quantities are made of the basic SI units.

Now, let’s look at our calculation. Joules can be expressed directly as kilograms, meters, and seconds. And seconds and meters per second are already basic SI units. So all we need to do is express kilohertz in terms of basic SI units. Recall that one kilohertz is exactly 10 to the third hertz. And this is exactly what we need because hertz are inverse second. So as long as we express 200 kilohertz in terms of just hertz, our units will be correct.

We make this correction by replacing kilohertz with 10 to the third hertz. Now that all of our units are correct. All we need to do is enter these numbers into a calculator. The result of this calculation is 4.42 times 10 to the negative 37. And this is already in scientific notation, and it only has two decimal places. For the units, since we made sure that all of the units in our original calculation could be expressed directly as basic SI units, our final answer will have units of momentum kilogram-meters per second.

The momentum of this low-frequency radio-wave photon is 4.42 times 10 to the negative 37 kilogram-meters per second.

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