Find the potential difference for which the error in the value of the momentum for the previous problem calculated using the nonrelativistic approximation does not exceed 5%. Do the calculations both for the electron and for the proton.

Find the potential difference for which the error in the value of the

1.	Find the potential difference for which the error in the value of the momentum for the previous problem calculated using the nonrelativistic approximation does not exceed 5%. Do the calculations both for the electron and for the proton.
Answer» <P> Solution :The RELATIVE error is `epsilon= (p_("rel")-p_("el"))/(p_("rel"))= 1-(csqrt(2qvarphim_(0)))/(SQRT(qvarphi(2E_(0)+qvarphi)))=1-sqrt((2E_(0))/(2E_(0)+qvarphi))` HENCE `varphi= (2E_(0))/(q).(2epsilon-epsilon^(2))/((1-epsilon)^(2))` Since `epsilon ltlt 1` we have `varphi= (4epsilonE_(0))/(q)`

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Find the potential difference for which the error in the value of the momentum for the previous problem calculated using the nonrelativistic approximation does not exceed 5%. Do the calculations both for the electron and for the proton.

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