Video Transcript
What is the wavelength of a photon
that has a momentum of 5.00 times 10 to the negative 25 kilogram meters per
second? Use a value of 6.63 times 10 to the
negative 34 joule-seconds for the Planck constant. Give your answer to two decimal
places.
This question asks us to find the
wavelength of a photon given its momentum. We can recall that the momentum of
a photon is defined as the Planck constant divided by its wavelength. And we can rearrange this formula
multiplying both sides by wavelength and dividing both sides by momentum to find the
wavelength of a photon is equal to the Planck constant divided by its momentum. Well, we are given a value for the
Planck constant and we are given a value for the momentum. So all that’s left to do is
substitute values. 6.63 times 10 to the negative 34
divided by 5.00 times 10 to the negative 25 is 1.326 times 10 to the negative
nine.
The units for this quantity are
joule-seconds divided by kilograms meters per second. We could work out what these units
are equivalent to by rewriting joules in terms of kilograms, meters, and seconds,
but there is a much simpler way. We are calculating a wavelength, so
the overall units must be appropriate for measuring length. Now, joules can be expressed
directly in terms of SI base units, and kilograms, meters, and seconds are
themselves SI base units. So the combination of all these
units must give another SI base unit, this time the SI base unit for length, which
is the meter. So the overall units of this
quantity are meters. So our wavelength is 1.326 times 10
to the negative nine meters.
When we round 1.326 to two decimal
places, we get 1.33. And just to make our answer a
little bit neater, we’ll recall that 10 to the negative nine meters is one
nanometer. So our final answer is 1.33
nanometers. This wavelength is much smaller
than the wavelength of a typical photon of visible light, which has a wavelength of
around 500 nanometers. So this photon must be a
high-energy X-ray or gamma ray.
