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A beam of electrons, travelling at [tex]9x10^6ms^{-1}[/tex] In every second, [tex]1x10^{14}[/tex] electrons hit a metal target and all their energy is converted into heat. How long would it take to heat up the metal from 18 degrees celsius to 80 degrees celsius if the heat capacity of the metal is [tex] 0.15JK^{-1}[/tex]. The mass of the electron is [tex]9x10^{-31} kg[/tex].

How i solved this problem was to find the momentum of each individual electron using the formula [tex]p=mv[/tex]. Then i found the energy of each electron using the relation [tex]E^2=(mc^2)^2+(pc)^2[/tex]. Then afterwards i found the heat energy in joules required to heat up the metal to 80 degrees celsius.

The thing is, i got 10.2 for the energy required to heat the metal object up. And the energy per second gained is [tex]8.08886[/tex]. Therefore the answer i got is 1.26 seconds. The problem is, the answer is [tex]1.44x10^5 s[/tex].

Where did I go wrong? I've got a feeling the momentum-energy relation in SR is a little outta place but I can't think of any other relation which relates momentum and energy. Thanks alot.

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# Homework Help: Heat and Electron question

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