Question
Uncertainty in position of a minute particle of mass $$25 g$$ in space is $${10^{ - 5}}\,m.$$ What is the uncertainty in its velocity ( in $$m{s^{ - 1}}$$ ) ?
$$\left( {h = 6.6 \times {{10}^{ - 34}}Js} \right)$$
A.
$$2.1 \times {10^{ - 34}}$$
B.
$$0.5 \times {10^{ - 34}}$$
C.
$$2.1 \times {10^{ - 28}}$$
D.
$$0.5 \times {10^{ - 23}}$$
Answer :
$$2.1 \times {10^{ - 28}}$$
Solution :
TIPS/Formulae :
$$\eqalign{
& \Delta x.\Delta p = \frac{h}{{4\pi }};\,\,\,{\text{or}}\,\,\Delta x.m.\Delta v = \frac{h}{{4\pi }} \cr
& \therefore \,\Delta v = \frac{{6.62 \times {{10}^{ - 34}}}}{{4 \times 3.14 \times 0.025 \times {{10}^{ - 5}}}} \cr
& = 2.1 \times {10^{ - 28}}m{s^{ - 1}} \cr} $$