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$-$34 Js)
Answer (integer)
22
Solution
<p>We know from hisenberg uncertainty principle</p>
<p>$\Delta x\,.\,\Delta p = {h \over {4\pi }}$</p>
<p>$\Rightarrow \Delta x\,.\,m\Delta v = {h \over {4\pi }}$</p>
<p>Given, </p>
<p>$\Delta$x = 10<sup>$-$7</sup> m</p>
<p>$\Delta$x = 2.4 $\times$ 10<sup>$-$26</sup> m/s</p>
<p>h = 6.626 $\times$ 10<sup>$-$34</sup> Js</p>
<p>$\therefore$ $${10^{ - 7}} \times m \times 2.4 \times {10^{ - 26}} = {{6.626 \times {{10}^{ - 34}}} \over {4\pi }}$$</p>
<p>$\Rightarrow 2.4m = {{6.626} \over {4\pi \times 10}}$</p>
<p>$\Rightarrow$ m = 0.022 kg</p>
<p>$\Rightarrow$ m = 22 gm</p>
About this question
Subject: Chemistry · Chapter: Atomic Structure · Topic: Bohr's Model
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