You are running an experiment that uses an accelerator that produces a 3.50-µA p
ID: 2010577 • Letter: Y
Question
You are running an experiment that uses an accelerator that produces a 3.50-µA proton beam. Each proton in the beam has 48.5-MeV of kinetic energy. The protons impinge on, and come to rest inside, a 51.0-g copper target within the vacuum chamber. You are concerned that the target will get too hot and melt the solder on some connecting wires that are crucial to the experiment.
(a) Determine the number of protons that strike the target per second.
? s-1
(b) Find the amount of energy delivered to the target each second.
? W
(c) Determine how much time elapses before the target temperature increases by 271° C. (Neglect any heat released by the target. The specific heat of copper is 0.386 kJ/kg · K.)
? s
Explanation / Answer
Here current I = 3.50*10^-6 A (a) The number of protons strike the target n = I /e e = charge of the proton n = 3.50*10-6 A / 1.6*10-19 C = 2.18*1013 (b) Amount of energy delivered to the target in each second is Power P = IV Here potential V = (Energy / charge) = ( 48.5 *106 (1.6*10-19 V)/ 1.6*10-19 C ) = 48.5*106 V P = ( 3.50*10-6 A)*(48.5*106 V) = 169.75 W (c) Energy delivered Q = Pt = mCcu T Time elapsed t = mCcu T / P Here P = power m = mass = 51*10^-3 kg change in temperature T = 271 0C Ccu = specific heat of copper = 0.386 K J /kg.K Then t = 31.42 sRelated Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.