JEE MAIN - Chemistry (2022 - 27th June Morning Shift - No. 11)
If the uncertainty in velocity and position of a minute particle in space are, 2.4 $$\times$$ 10$$-$$26 (m s$$-$$1) and 10$$-$$7 (m) respectively. The mass of the particle in g is ____________. (Nearest integer)
(Given : h = 6.626 $$\times$$ 10$$-$$34 Js)
Answer
22
Explanation
We know from hisenberg uncertainty principle
$$\Delta x\,.\,\Delta p = {h \over {4\pi }}$$
$$ \Rightarrow \Delta x\,.\,m\Delta v = {h \over {4\pi }}$$
Given,
$$\Delta$$x = 10$$-$$7 m
$$\Delta$$x = 2.4 $$\times$$ 10$$-$$26 m/s
h = 6.626 $$\times$$ 10$$-$$34 Js
$$\therefore$$ $${10^{ - 7}} \times m \times 2.4 \times {10^{ - 26}} = {{6.626 \times {{10}^{ - 34}}} \over {4\pi }}$$
$$ \Rightarrow 2.4m = {{6.626} \over {4\pi \times 10}}$$
$$\Rightarrow$$ m = 0.022 kg
$$\Rightarrow$$ m = 22 gm
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