If the uncertainty in velocity and position of a minute part

Question

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)

DivineJEE · Accepted Answer

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

Explanation

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