Question

Uncertanity in the position of an electron (mass= 9.1 x ${10}^{-31}$ kg) moving with velocity $300m{s}^{-1}$, accurate upto 0.001%, will be (h = 6.63 x ${10}^{-34}$ JS) :

• A. 19.2 x ${10}^{-2}$ m
• B. 5.76 x ${10}^{-2}$ m
• C. 1.92 x ${10}^{-2}$ m
• D. 3.83 x ${10}^{-2}$ m

Answer 1

The correct option is C 1.92 x ${10}^{-2}$ m

Use,
$\Delta x=h/4\pi m\Delta v$.
Use, $\Delta v=0.001/100\times 300m/s=3\times {10}^{-3}m/s$.
$\Delta x=6.6\times {10}^{-34}/(4\pi \times 9.1\times {10}^{-31}\times 3\times {10}^{-3})m=1.9\times {10}^{-2}m$.