Structure of Atom - Result Question 27
####29. Given : The mass of electron is $9.11 \times 10^{-31} kg$ Planck constant is $6.626 \times 10^{-34} Js$, the uncertainty involved in the measurement of velocity within a distance of $0.1 \AA$ is [2006]
(a) $5.79 \times 10^{7} ms^{-1}$
(b) $5.79 \times 10^{8} ms^{-1}$
(c) $5.79 \times 10^{5} ms^{-1}$
(d) $5.79 \times 10^{6} ms^{-1}$
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Solution:
- (d) We know that $\Delta x . \Delta p \geq \frac{h}{4 \pi}$
$\Delta x . m \Delta v>\frac{h}{4 \pi}$
$\Delta v>\frac{h}{4 \pi \Delta x m}$
$ \begin{aligned} \Delta v & =\frac{6.626 \times 10^{-34}}{4 \pi \times 0.1 \times 10^{-10} \times 9.11 \times 10^{-31}} \\ & =\frac{66}{4 \pi \times 9} \times 10^{7}=5.79 \times 10^{6} m / sec \end{aligned} $
