Answer

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**Hint:**This question is based on Heisenberg’s uncertainty principle which can be mathematically written as -

$\Delta x \times \Delta p \geqslant \dfrac{h}{{2\Pi }}$

Where Δx is the uncertainty in position

Δp is the change in momentum

H is the Planck's constant

Further, the moment is the product of the mass of the moving object and the velocity with which it is moving.

**Complete step by step answer :**

This question is based on Heisenberg’s uncertainty principle which states that it is impossible to measure the position and momentum of a body simultaneously with absolute precision.

Mathematically, it can be written as -

$\Delta x \times \Delta p \geqslant \dfrac{h}{{2\Pi }}$

Where Δx is the uncertainty in position

Δp is the change in momentum

H is the Planck's constant

On filling the value of p = mv

We can write it as -

$\Delta x \times m\Delta v \geqslant \dfrac{h}{{2\Pi }}$

Where m is the mass of the moving object

And v is the velocity of the object.

Now, let us see the values given to us and what we need to find out.

Given :

Size of a microscopic particle = 1 micron

Mass of the microscopic particle (m) = $6 \times {10^{ - 13}}$g

Δx = 0.1% of size of the particle

Δx = $\dfrac{{0.1}}{{100}} \times {10^{ - 4}}$

Δx = ${10^{ - 7}}cm$

To find :

Uncertainty in velocity (in $c{m^{ - 1}}$) -

Now, filling all the values in the above formula, we get,

${10^{ - 7}} \times 6 \times {10^{ - 13}}\Delta v$ = $\dfrac{h}{{4\Pi }}$

On solving the above equation, we get -

Δv = $\dfrac{{6.626 \times {{10}^{ - 34}}}}{{4 \times 3.14 \times {{10}^{ - 7}} \times 6 \times {{10}^{ - 13}}}}$

Δv = $0.276 \times {10^{ - 14}}c{m^{ - 1}}$

If we see the above options, then none of these matches are answered.

**So, none of the options given is correct.**

**Note:**The momentum of a moving object is the product of the mass of the moving object and the velocity with which it is moving. Heisenberg’s uncertainty principle is applicable to only microscopic particles.

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