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This is College Physics Answers
with Shaun Dychko.
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A proton emerges from a Van de Graaff
accelerator with a velocity of
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25 percent the speed of light
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and the first question is,
what is its wavelength?
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So that is going to be
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Planck's constant divided by its momentum
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and since we are told that
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its velocity is non-relativistic,
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we'll say that the momentum is
mass times velocity
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which we can then replace *p* with.
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So lambda then is Planck's constant
over mass times velocity.
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So we have Planck's constant divided
by the mass of a proton
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times 0.250 times the speed of light,
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which gives 5.29 femtometers,
is its de Broglie wavelength.
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Its kinetic energy is one-half mass
times velocity squared
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so that's one-half times mass of a proton
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times 0.250 times the speed
of light, all squared,
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giving 4.7 times 10 to the minus
12 joules of kinetic energy.
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Then in part (c), we are asked to
figure out what voltage
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must it have been accelerated through?
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Well, all of this kinetic energy
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was given to the proton by this
potential difference
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and that amount of energy will be the
potential difference times the charge.
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And so we'll divide both sides
by the charge *q*.
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And so we get the voltage is the
kinetic energy divided by *q*.
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So this is the kinetic energy we found
in part (b),
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divided by the elementary charge
in a proton
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which is 29.3 megavolts.