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# The speed of a certain proton is $4.5\times10^5m$ If the uncertainity is to be reduced to 0.01percent, what uncertainity in its location must be tolerated?

$(a)\;0.70nm\qquad(b)\;0.60nm\qquad(c)\;0.40nm\qquad(d)\;0.80nm$

Can you answer this question?

V=$4.5\times10^5$m/sec
$\bigtriangleup V= V\times \large\frac{0.01}{100}$
$=4.5\times10$
=45m/sec
$\bigtriangleup x .\bigtriangleup V \approx \large\frac{h}{4\pi m}$
$\bigtriangleup x = \large\frac{h}{4\pi m\bigtriangleup V}$
$=\large\frac{6.626\times10^{-34}}{4\pi\times1.673\times10^{-27}\times27}$
$=7\times10^{-10}$
=0.70nm
Hence the anwer is (a)
answered Feb 5, 2014