A cyclotron produces a beam of protons that have meV Of energy. The protons coll

Question

A cyclotron produces a beam of protons that have meV Of energy. The protons collide with a 50 g copper disc In a vacuum chamber and come to rest. a) If the target gains 3.5*10^-6 Coulombs of charge per second from collisions, how many protons per second is the is the cyclotron emitting? b) At what rate is energy being deposited into the copper target? c) Use the result from b) and Q = mcDeltaT to caculate how long it will take for the target's temperature to increase by 300 degrees Celsius. Q is measured in Joules, DeltaT represent the change in temperature, m is the mass of the target and C is the specific heat of Copper (c = 0.385 J/g degree C). Ignore radiative losses as the target heats.

Explanation / Answer

(a) given that i = 3.5 * 10^-6 amp

no. of proton colliding per second be N than ; N e =i : e =1.6*10^-19C

or N = i /e = 3.5*10^-6 / 1.6*10^-19 = 2.18175 * 10^13 PER SECOND

(b) Each proton has energy Eo = 60MeV = 60*10^6 * 1.6* 10^-19 Jso

power transmitted (or energy being deposited to Cu plate ) P = N * Eo = 210 W

(c) Every second P amount of energy is being deposited to Cu plate

so if t be the time required to raise the temp. by T

than mST =Pt

hence t = mST/P = (50 *0.385 *300) /210 = 27.5 seconds

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