Answer :
Answer:
The correct question is:
"Find the energy each gains"
The energy gained by a charged particle accelerated through a potential difference is given by
[tex]\Delta U = q\Delta V[/tex]
where
q is the charge of the particle
[tex]\Delta V[/tex] is the potential difference
For a proton,
[tex]q=+e=1.6\cdot 10^{-19}C[/tex]
And since [tex]\Delta V=100 V[/tex]
The energy gained by the proton is
[tex]\Delta U=(1.6\cdot 10^{-19})(100)=1.6\cdot 10^{-17}J[/tex]
For an alpha particle,
[tex]q=+2e=3.2\cdot 10^{-19}C[/tex]
Therefore, the energy gained is
[tex]\Delta U=(3.2\cdot 10^{-19})(100)=3.2\cdot 10^{-17}J[/tex]
Finally, for a singly ionized helium nucleus (a helium nucleus that has lost one electron)
[tex]q=+e=1.6\cdot 10^{-19}C[/tex]
So the energy gained is the same as the proton:
[tex]\Delta U=(1.6\cdot 10^{-19})(100)=1.6\cdot 10^{-17}J[/tex]
The energy that proton and alpha particle is [tex]1.6\times 10^{-17}{\rm J[/tex] and [tex]3.2\times 10^{-17}{\rm J[/tex] respectively.
The energy gained by proton can be determined by,
[tex]\Delta U = q \times \Delta V[/tex]
Where,
[tex]\Delta U[/tex] - energy gained
[tex]q[/tex] - charge = [tex]1.6\times 10^{-19}\rm C[/tex]
[tex]\Delta V[/tex] - change in velocity = 100 V
Put the values,
[tex]\Delta U =1.6\times 10^{-19}{\rm C }\times 100 \rm \ V\\\\\Delta U = 1.6\times 10^{-17}{\rm J }[/tex]
Since, an alpha particle has 2 protons, hence they have two times higher energy ([tex]3.2\times 10^{-17}{\rm J }[/tex]).
Therefore, the energy that proton and alpha particle is [tex]1.6\times 10^{-17}{\rm J[/tex] and [tex]3.2\times 10^{-17}{\rm J[/tex] respectively.
To know more about charge of particles,
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