JEE MAIN - Chemistry (2009 - No. 24)
In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity
with which the position of the electron can be located is (h = 6.6 $$\times$$ 10-34 kg m2s-1, mass of electron, em = 9.1 $$\times$$ 10-31 kg)
5.10 $$\times$$ 10-3 m
1.92 $$\times$$ 10-3 m
3.84 $$\times$$ 10-3 m
1.52 $$\times$$ 10-4 m
Explanation
% error in velocity = $${{\Delta V} \over V} \times 100$$
$$ \therefore $$ 0.005 = $${{\Delta V} \over {600}} \times 100$$
$$ \Rightarrow $$ $$\Delta $$V = 3 $$ \times $$ 10-2
According to Heisenberg uncertainty principle,
$$\Delta x.m\Delta V \ge {h \over {4\pi }}$$
$$ \Rightarrow $$ $$\Delta x = {h \over {4\pi m\Delta V}}$$
$$ \Rightarrow $$ $$\Delta x = {{6.63 \times {{10}^{ - 34}}} \over {4 \times 3.14 \times 9.1 \times {{10}^{ - 31}} \times 3 \times {{10}^{ - 2}}}}$$
= 1.92 $$ \times $$ 10-3 m
$$ \therefore $$ 0.005 = $${{\Delta V} \over {600}} \times 100$$
$$ \Rightarrow $$ $$\Delta $$V = 3 $$ \times $$ 10-2
According to Heisenberg uncertainty principle,
$$\Delta x.m\Delta V \ge {h \over {4\pi }}$$
$$ \Rightarrow $$ $$\Delta x = {h \over {4\pi m\Delta V}}$$
$$ \Rightarrow $$ $$\Delta x = {{6.63 \times {{10}^{ - 34}}} \over {4 \times 3.14 \times 9.1 \times {{10}^{ - 31}} \times 3 \times {{10}^{ - 2}}}}$$
= 1.92 $$ \times $$ 10-3 m
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