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.
