Question
What will be the mass of a particle if uncertainty in its posttton is $${10^{ - 8}}\,m$$ and velocity is $$5.26 \times {10^{ - 25}}\,m\,{s^{ - 1}}\,?$$
A.
0.01$$\,kg$$
B.
0.1$$\,kg$$
C.
1$$\,kg$$
D.
10$$\,kg$$
Answer :
0.01$$\,kg$$
Solution :
$$\Delta x \cdot m\Delta v = \frac{h}{{4\pi }}$$
$${10^{ - 8}}\,m \times m \times 5.26 \times {10^{ - 25}}\,m\,{s^{ - 1}}$$ $$ = \frac{{6.626 \times {{10}^{ - 34}}\,J\,s}}{{4 \times 3.14}}$$
$$\eqalign{
& m = \frac{{6.626 \times {{10}^{ - 34}}\,J\,s}}{{4 \times 3.14 \times {{10}^{ - 8}}\,m \times 5.26 \times {{10}^{ - 25}}\,m\,{s^{ - 1}}}} \cr
& \,\,\,\,\,\, = 0.01\,kg \cr} $$