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Question Video: Calculating the Energy of a Photon Given Its Frequency Physics • 9th Grade

What is the energy of a photon that has a frequency of 5 × 10¹⁵ Hz? Use 4.14 × 10⁻¹⁵ eV⋅s for the value of the Planck constant. Give your answer in electron volts to one decimal place.

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Video Transcript

What is the energy of a photon that has a frequency of five times 10 to the power of 15 hertz? Use 4.14 times 10 to the power of minus 15 electron-volt seconds for the value of the Planck constant. Give your answer in electron volts to one decimal place.

This question is asking us to find the energy of a photon, given its frequency. To do this, we simply need to recall the formula 𝐸 equals ℎ𝑓. The energy, 𝐸, of the photon is equal to the Planck constant, ℎ, multiplied by the frequency of the photon, 𝑓. We’re told that the frequency of the photon is five times 10 to the power 15 hertz and that we can use a value of 4.14 times 10 to the power of minus 15 electron-volt seconds for the Planck constant.

So, to answer this question, all we need to do is substitute these values into our formula. Doing this, we find that the energy of the photon is equal to 4.14 times 10 to the power of minus 15 electron-volt seconds multiplied by five times 10 to the power 15 hertz.

Before we work out this value, let’s quickly check that we’re working with the right units. On the right-hand side of our expression, we have units of electron-volt seconds multiplied by hertz. However, we can recall that the units of hertz are equivalent to inverse seconds, or seconds to the power of minus one. If we replace the units of hertz in our expression with units of inverse seconds, we see that the two seconds terms cancel each other out, leaving us with units of electron volts, a common unit for measuring energy of photons. We’re now ready to complete this calculation.

If we multiply through these values, we find that the energy of the photon is equal to 20.7 electron volts. This is our final answer to this question. 20.7 electron volts is the energy of a photon that has a frequency of five times 10 to the power of 15 hertz.

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