Physics: Abeam of protons is moving toward a target in a particle accelerator. this beam constitutes a current whose value is 0.50 μa. (a) how many protons strike the target in 15 s? (b) each proton has a kinetic energy of 4.9 x 10-12 j. suppose the target is a 15 gram block of aluminum, and all the kinetic energy of the protons goes into heating it up. what is the change in temperature of the block that results from 15 s bombardment of protons?

Abeam of protons is moving toward a target in

Ответ:

xXCoryxKenshinXx

13.03.2022

(a) The current is defined as the amount of charge that strikes the target per unit time:
$I= \frac{Q}{t}$
where Q is the total charge and t the time.
We know the current, $I=0.50 \mu A=0.5 \cdot 10^{-6}A$ , and the time, t=15 s

, so we can calculate the amount of charge that strikes the target during this time interval:
$Q=It=(0.5 \cdot 10^{-6} A)(15 s)=7.5 \cdot 10^{-6}C$

We know that each proton has a charge of $q=1.6 \cdot 10^{-19}C$ , so if we divide the total charge Q by the charge of one proton q, we find the number of protons that strike the target:
$N= \frac{Q}{q}= \frac{7.5 \cdot 10^{-6} C}{1.6 \cdot 10^{-19}C}=4.7 \cdot 10^{13}$

(b) The total energy given by the beam of protons to the block of aluminium is equal to the kinetic energy of one proton times the number of protons:
$E=NK=(4.7 \cdot 10^{13})(4.9 \cdot 10^{-12}J)=230.3 J$

This energy is given as heat to the block of aluminium, and the increase in temperature of the block is related to this energy by
$E=mC_s \Delta T$
where m=15 g=0.015 kg is the mass of the block, $C_s=900 J/kg^{\circ}C$ is the specific heat capacity of aluminium, and $\Delta T$ is the increase in temperature that we want to find.

If we rearrange the equation, we find $\Delta T$ :
$\Delta T= \frac{E}{mC_s}= \frac{230.3 J}{(900 J/kg^{\circ})(0.015 kg)} =17.0^{\circ}C$