Question

By use of Heisenberg uncertainty principle determine uncertainty in position for a hydrogen molecule moving at a speed of $2 \cdot 0 \times 10^{6} cm / s$. (Mass of $H_{2}=3.3474 \times 10^{-24} g$ ).

Answer 1

SOLUTION : The mass of $H _{2}$ molecule is in five significant figures, i.e, error in the mass $=0.0001 \times 10^{-24} g$. Since the velocity is given to two significant figures,

we may assume that the error in the velocity is $0.1 \times 10^{8} cms ^{-1}$.

The error in the momentum is approximately equal to $\Delta p=1 \times 10^{-28} \times 0 \cdot 1 \times 10^{8}=1 \cdot 0 \times 10^{-21}$

$\Delta x=\frac{h}{4 \pi \times \Delta p}=\frac{6 \cdot 626 \times 10^{-27}}{4 \times 3 \cdot 1416 \times 1 \cdot 0 \times 10^{-21}}=5 \cdot 27 \times 10^{-7} c m \text {. }$