A proton is accelerated to 1/10th of the velocity of light. If its velocity can be measured with a precision of +- 0.5%, what must be its uncertanity in position?

A proton is accelerated to 1/10th of the velocity of light. If its vel

1.	A proton is accelerated to 1/10th of the velocity of light. If its velocity can be measured with a precision of +- 0.5%, what must be its uncertanity in position?
Answer» Solution :Velocity of LIGHT `= 3 xx 10^(8) ms^(-1)` `:.` Velocity of proton `= (1)/(10) xx 3 xx 10^(8) = 3 xx 10^(7) ms^(-1)` `Delta v = (0.5)/(100) xx 3 xx 10^(7) = 1.5 xx 10^(5) ms^(-1)` Applying Heisenberg's uncertanity principle. `Delta x. m Delta v = (h)/(4pi)` We get `Delta x = (h)/(4pi xx m Delta v) = (6.626 xx 10^(-34) kg m^(2) s^(-1))/(4 xx 31.43 xx 1.66 xx 10^(-27) kg xx 1.5 xx 10^(5) ms^(-1)) = 2.11 xx 10^(-13) m`