For many, many years, the radius of a proton has been considered to be 0.877 fm.
ID: 1534269 • Letter: F
Question
For many, many years, the radius of a proton has been considered to be 0.877 fm. New experiments that were just published in the journal science (using an short-lived creation called "muonic hydrogen") have shown that the radius that the radius of a proton is actually 0.841 fm. Although this might not seem like a big difference, this new data is well outside standard "error bars" of previous experiments. Perhaps there is new physics still yet discovered? The world still waits to see... Darth Maul, though, decides to do some experiments to test new ideas with his proton gun. His proton gun uses a parallel plats capacitor (with a small hole in one of the plates) to shoot protons out of it at high velocities. His fires these protons at a chlorine nucleus from a very large distance away from it. He varies the voltage used to accelerate the proton unit it will just barely 'touch' the nucleus in question. The nucleus can be assumed to behave like a point charge with Q = + 17e and radius 3.921 fm. If the radius of a proton is 0.877 fm, what voltage (in MegaVolts) must Darth Maul set his proton gun to fire? If the radius of a proton is 0.841 fm, what voltage (in MegaVolts) must Darth Maul set his proton gun to fire? Analysis: If you are very careful with your math, you should see that there is indeed a very small difference in the voltage required for the proton and nucleus to touch...Explanation / Answer
Proton Original radius = r1 =0.877 fm= 0.877 x 10-15m
Proton New radius = r2= 0.841 fm = 0.841 x 10-15m
Nucleus radius = 3.921 fm= 3.921 x 10-15m
Charge of nucleus = Q= 17e = 17 x 1.6 x 10-19c
Work done by high voltage = Potential energy of proton nucleus system
q V = k Q q / ( r+ R)
k= 9 x 109
V= k Q /( r+R)
(a) r = 0.877 x 10-15m
V = (9 x 109 x 17 x 1.6 x 10-19)/( 0.877 x 10-15 + 3.921 x 10-15)
=10 5 x (9 x 17 x 1.6)/(0 .877 + 3.92)
=5.103 x 106V
=5.103 MV
(b)r= 0.841 x 10-15m
V = (9 x 109 x 17 x 1.6 x 10-19)/( 0.841 x 10-15 + 3.921 x 10-15)
=10 5 x (9 x 17 x 1.6)/( 0.841 + 3.92)
=5.141 x 106V
=5.141 MV
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.