AP EAMCET · Chemistry · Structure of Atom

If $Δx$ is the uncertainity in position and $Δv$ is the uncertainity in velocity of a particle are equal, the correct expression for uncertainity in momentum for the same particle is

A $\frac{1}{4} \sqrt{\frac{m h}{π}}$
B $\frac{1}{3} \sqrt{\frac{m h}{2 π}}$
C $\frac{1}{2} \sqrt{\frac{m h}{π}}$
D $\frac{1}{2} \sqrt{\frac{h}{m π}}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{1}{2} \sqrt{\frac{m h}{π}}$

Step-by-step Solution

Detailed explanation

The uncertainty in momentum and uncertainty in the position of a particle are equal. So, ∆v=∆x According to the uncertainty principle, The uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or electron, with…

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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If Δx is the uncertainity in position and Δv is the uncertainity in velocity of a particle are equal, the correct expression for uncertainity in momentum for the same particle is

Step-by-step Solution

If $Δx$ is the uncertainity in position and $Δv$ is the uncertainity in velocity of a particle are equal, the correct expression for uncertainity in momentum for the same particle is