Question
What will be the uncertainty in velocity of an electron when the uncertainty in its position is $$1000\,\mathop {\text{A}}\limits^{\text{o}} ?$$
A.
$$5.79 \times {10^2}\,m\,{s^{ - 1}}$$
B.
$$5.79 \times {10^8}\,m\,{s^{ - 1}}$$
C.
$$5.79 \times {10^4}\,m\,{s^{ - 1}}$$
D.
$$5.79 \times {10^{ - 10}}\,m\,{s^{ - 1}}$$
Answer :
$$5.79 \times {10^2}\,m\,{s^{ - 1}}$$
Solution :
$$\Delta x \cdot m\Delta v = \frac{h}{{4\pi }}$$
$$\Delta x = 1000\,\mathop {\text{A}}\limits^{\text{o}} = 1000 \times {10^{ - 10}}\,m\,\,\,$$ $${\text{or}}\,\,\,{10^{ - 7}}\,m$$
$$\eqalign{
& \Delta v = \frac{{6.626 \times {{10}^{ - 34}}\,J\,s}}{{4 \times 3.14 \times 9.1 \times {{10}^{ - 31}}\,kg \times {{10}^{ - 7}}\,m}} \cr
& \,\,\,\,\,\,\,\, = 5.79 \times {10^2}\,m/s \cr} $$