The product of uncertainty in the position and uncertainty in the velocity of a particle is 5.79×10-5 m2 s-1. If the uncertainty in the position is 1nm, what is the uncertainty in the measurement of its velocity in ms-1?

TS EAMCET · Chemistry · Structure of Atom

The product of uncertainty in the position and uncertainty in the velocity of a particle is $5.79 \times 10^{- 5} m^{2} s^{- 1} .$ If the uncertainty in the position is $1 nm$ , what is the uncertainty in the measurement of its velocity in ${ms}^{- 1} ?$

A $5.79 \times 10^{7}$
B $5.79 \times 10^{5}$
C $5.79 \times 10^{- 5}$
D $5.79 \times 10^{4}$

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Answer & Solution

Correct Answer

(D) $5.79 \times 10^{4}$

Step-by-step Solution

Detailed explanation

Heisenberg's principle : The exact position and momentum of a fast moving particle cannot be calculated exactly at the same moment of time. As per Heisenberg's uncertainty principle, ∆x.∆p = h4π ∆p=Uncertainty in momentum ∆p=m∆v…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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