WEBVTT
00:00:00.000 --> 00:00:02.840
This is College Physics Answers
with Shaun Dychko.
00:00:03.140 --> 00:00:07.280
A 50 kilovolt x-ray tube
accelerates electrons
00:00:07.485 --> 00:00:12.594
and the maximum energy of the photon
emitted by this x-ray tube
00:00:12.590 --> 00:00:15.897
will be equal to the kinetic energy
of the electrons.
00:00:16.411 --> 00:00:18.560
And that's gonna be the electron charge
00:00:18.560 --> 00:00:21.302
multiplied by the voltage through
which it is accelerated.
00:00:22.160 --> 00:00:25.040
And so we can equate the energy
which we can write as
00:00:25.040 --> 00:00:28.068
Planck's constant times speed of light
divided by lambda
00:00:28.060 --> 00:00:31.531
and you can equate that to *qV*.
00:00:33.085 --> 00:00:37.177
And let's solve this for lambda by taking
the reciprocal of both sides
00:00:37.691 --> 00:00:40.251
so this *λ* over *hc* equals 1 over *qV*
00:00:40.251 --> 00:00:42.250
and then multiply both sides by *hc*.
00:00:43.200 --> 00:00:47.691
So we have the shortest possible
wavelength is *hc* over *qV*.
00:00:47.690 --> 00:00:51.794
So that's 6.626 times 10 to the minus 34
joule seconds—Planck's constant—
00:00:51.790 --> 00:00:54.274
times speed of light divided by
elementary charge
00:00:54.270 --> 00:00:56.377
times 50 times 10 to the 3 volts
00:00:56.370 --> 00:01:01.657
giving 2.48 times 10 to the minus 11 meters
is the shortest possible wavelength.
00:01:03.417 --> 00:01:06.925
And then in part (b), we calculate
the energy of this wavelength
00:01:06.920 --> 00:01:09.702
and that's *hc* divided by *λ*
00:01:09.700 --> 00:01:14.445
and *hc* we are going to take to be
1240 electron volt nanometers
00:01:14.440 --> 00:01:16.628
and so we'll divide by this wavelength
00:01:16.620 --> 00:01:18.617
also expressed in units of nanometers
00:01:18.610 --> 00:01:22.365
so that these nanometers cancel and
we'll get an answer in electron volts.
00:01:22.360 --> 00:01:26.788
So this written in nanometers is
0.02480 nanometers
00:01:27.108 --> 00:01:30.697
and this works out to 50.0 kiloelectron volts.
00:01:31.440 --> 00:01:33.977
And in part (c), we talk about
00:01:33.970 --> 00:01:37.897
how this corresponds to this
00:01:37.890 --> 00:01:41.634
this is the voltage of the x-ray tube—
50 kilovolts—
00:01:41.630 --> 00:01:45.668
and this is the maximum energy
photon emitted
00:01:46.171 --> 00:01:50.480
and the maximum photon energy
00:01:50.480 --> 00:01:52.857
is the kinetic energy of the electron
00:01:52.850 --> 00:01:57.120
which is *q* times *V* and this is
the elementary charge
00:01:57.360 --> 00:02:01.714
of an electron multiplied by the voltage
so that makes electron volts
00:02:01.897 --> 00:02:06.331
and therefore, we see that the
maximum photon energy is
00:02:06.330 --> 00:02:09.737
the x-ray tube voltage written in
units of electron volts.
00:02:09.885 --> 00:02:12.491
So where we started with 50 kilovolts,
00:02:12.490 --> 00:02:15.622
we can write that as 50 kiloelectron volts
00:02:15.620 --> 00:02:18.365
for calculating the maximum photon energy.