A proton, an alpha particle (a bare helium nucleus), and a singly ionized helium atom are accelerated through a potential difference of 100 V. Find the energy that proton gains..

The energy that proton and alpha particle is and respectively.

The energy gained by proton can be determined by,

Where,

-  energy gained

- charge =

- change in velocity  = 100 V

Put the values,

Since, an alpha particle has  2 protons, hence they have two times higher energy ().

Therefore, the energy that proton and alpha particle is and respectively.

To know more about charge of particles,

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The correct question is:

"Find the energy each gains"

The energy gained by a charged particle accelerated through a potential difference is given by

where

q is the charge of the particle

is the potential difference

For a proton,

And since

The energy gained by the proton is

For an alpha particle,

Therefore, the energy gained is

Finally, for a singly ionized helium nucleus (a helium nucleus that has lost one electron)

So the energy gained is the same as the proton:

work: w = fd (given)

work done by chet   =50*1 = 50 j

work done by mika =40*2 = 80 j

work done by sara =30*1.5 = 45 j

work done by bill =60*0.5 = 30 j

students in order from the greatest amount of work done to the least is mika> chet> sara> bill

hence option (b) is correct.