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CBSE Class 12-science Answered

A proton and an alpha particle enter a uniform magnetic field perpendicularly with the same speed. How many times is the time period of the alpha particle than that of the proton? Also find the ratio of the radii of the circular path of the two particles?
Asked by Topperlearning User | 19 May, 2015, 03:30: PM
answered-by-expert Expert Answer

Time period of revolution is given as,

 begin mathsize 11px style straight T space equals space fraction numerator 2 πm over denominator Bq end fraction end style

Let  mp = mass of the proton

       mα = mass of the alpha particle.

       qp = charge of the proton

       qα = charge of the alpha particle.

For proton: time period,

begin mathsize 11px style straight T subscript 1 space equals space fraction numerator 2 πm subscript straight p over denominator Bq subscript straight p end fraction equals space fraction numerator 2 πm over denominator Bq end fraction end style

For alpha particle: time period,

Syntax error from line 1 column 55 to line 1 column 96. Unexpected 'mathvariant'.

=>begin mathsize 11px style fraction numerator 2 straight pi left parenthesis 4 straight m right parenthesis over denominator straight B left parenthesis 2 straight q right parenthesis end fraction equals space 2 open parentheses fraction numerator 2 πm over denominator Bq end fraction close parentheses space equals space 2 straight T subscript 1 space left parenthesis straight m subscript straight alpha space equals space 4 straight m subscript straight p comma straight q subscript straight alpha equals 2 straight q subscript straight p right parenthesis end style

As begin mathsize 11px style straight r equals mv over Bq end style

So,

begin mathsize 11px style straight r proportional to straight m over straight q end style

Therefore,

=>

Answered by | 19 May, 2015, 05:30: PM

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