Find the ratio of the Linear moment acquired by an alpha particle and a proton accelerated through same potential ?

Asked by Deepak Singh | 1st Jun, 2015, 10:09: AM

Expert Answer:

begin mathsize 14px style For space alpha space particle comma space mass space equals space 4 space straight a. straight m. straight u space and space charge comma space straight q space equals 2 straight e For space proton comma space mass space equals 1 space straight a. straight m. straight u comma space charge comma space straight q space equals straight e As space the space charged space particle space are space moving space through space same space potential comma the space kinetic space energy space aquired space by space the space particle space will space be space equal space to space the space electric space potential space energy straight i. straight e 1 half mv squared space equals qV where space straight V space is space the space potential comma space straight q space the space charge comma space straight m space the space mass space of space the space particle space and space straight v space the space velocity space of space the space partcle. But space we space know space that space the space momentum comma straight p equals mv rightwards double arrow 1 half mv squared space equals qV equals fraction numerator straight P squared over denominator 2 straight m end fraction rightwards double arrow straight P equals square root of 2 mqV end root Let space straight P subscript straight p space be space the space momentum space of space the space proton space and space straight P subscript straight alpha space that space of space the space proton Then colon straight P subscript straight alpha over straight P subscript straight p equals fraction numerator square root of 2 straight m subscript straight alpha space straight q subscript straight alpha space straight V end root over denominator square root of 2 straight m subscript straight p space straight q subscript straight p space straight V end root end fraction rightwards double arrow straight P subscript straight alpha over straight P subscript straight p space equals fraction numerator square root of 2 cross times 4 space straight a. straight m. straight u cross times 2 space straight e end root over denominator square root of 2 cross times 1 space straight a. straight m. straight u cross times space straight e end root end fraction rightwards double arrow straight P subscript straight alpha over straight P subscript straight p space equals fraction numerator square root of 8 over denominator 1 end fraction end style

Answered by Jyothi Nair | 1st Jun, 2015, 01:26: PM

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