JEE MAIN - Chemistry (2006 - No. 44)
Uncertainty in the position of an electron (mass = 9.1 $$\times$$ 10-31 kg) moving with a velocity 300 ms-1, accurate upto 0.001% will be (h = 6.63 $$\times$$ 10-34 Js)
1.92 $$\times$$ 10-2 m
3.84 $$\times$$ 10-2 m
19.2 $$\times$$ 10-2 m
5.76 $$\times$$ 10-2 m
Explanation
% error in velocity = $${{\Delta V} \over V} \times 100$$
$$ \therefore $$ 0.001 = $${{\Delta V} \over {300}} \times 100$$
$$ \Rightarrow $$ $$\Delta $$V = 3 $$ \times $$ 10-3
According to Heisenberg uncertainty principle,
$$\Delta x.m\Delta V \ge {h \over {4\pi }}$$
$$ \Rightarrow $$ $$\Delta x = {h \over {4\pi m\Delta V}}$$
$$ \Rightarrow $$ $$\Delta x = {{6.63 \times {{10}^{ - 34}}} \over {4 \times 3.14 \times 9.1 \times {{10}^{ - 31}} \times 3 \times {{10}^{ - 3}}}}$$
= 1.92 $$ \times $$ 10-2 m
$$ \therefore $$ 0.001 = $${{\Delta V} \over {300}} \times 100$$
$$ \Rightarrow $$ $$\Delta $$V = 3 $$ \times $$ 10-3
According to Heisenberg uncertainty principle,
$$\Delta x.m\Delta V \ge {h \over {4\pi }}$$
$$ \Rightarrow $$ $$\Delta x = {h \over {4\pi m\Delta V}}$$
$$ \Rightarrow $$ $$\Delta x = {{6.63 \times {{10}^{ - 34}}} \over {4 \times 3.14 \times 9.1 \times {{10}^{ - 31}} \times 3 \times {{10}^{ - 3}}}}$$
= 1.92 $$ \times $$ 10-2 m
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