Structure of Atom - Result Question 30
####32. Uncertainty in position of an electron $(.$ mass $.=9.1 \times 10^{-28} g)$ moving with a velocity of $3 \times 10^{4} cm / s$ accurate upto $0.001 %$ will be (use $h / 4(\pi)$ in uncertainty expression where $h=6.626 \times 10^{-27}$ erg-second)
[1995]
(a) $1.93 cm$
(b) $3.84 cm$
(c) $5.76 cm$
(d) $7.68 cm$
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Solution:
- (a) Given mass of an electron $(m)=9.1 \times 10^{-28} g$; Velocity of electron $(v)=3 \times 10^{4} cm / s$;
Accuracy in velocity $=0.001 %=\frac{0.001}{100}$;
Actual velocity of the electron
$(\Delta v)=3 \times 10^{4} \times \frac{0.001}{100}=0.3 cm / s$.
Planck’s constant $(h)=6.626 \times 10^{-27}$ erg-sec. $\therefore$ Uncertainty in the position of the electron
$ (\Delta x)=\frac{h}{4 \pi m \Delta v}=\frac{6.626 \times 10^{-27} \times 7}{\begin{matrix} 4 \times 22 \times(9.1 \times 10^{-28}) \times 0.3 \\ =1.93 cm \end{matrix} } $
