JEE Mains · Chemistry · STD 11 - 2. structure of atom

The minimum uncertainty in the speed of an electron in an one dimensional region of length \(2 a _{ o }\) (Where \(a _{0}=\) Bohr radius \(52.9 pm\) ) is \(km s ^{-1}\) (Given : Mass of electron \(=9.1 \times 10^{-31} kg\), Planck's constant \(h =6.63 \times 10^{-34} \;Js\) )

A \(548\)
B \(547\)
C \(546\)
D \(545\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(548\)

Step-by-step Solution

Detailed explanation

Heisenberg's uncertainty principle \(\Delta x \times \Delta p _{ x } \geq \frac{ h }{4 \pi}\) \(\Rightarrow 2 a _{0} \times m \Delta v _{ r }=\frac{ h }{4 \pi}(\text { minimum })\) \(\Rightarrow \Delta v _{ x}=\frac{ h }{4 \pi} \times \frac{1}{2 a _{0}} \times \frac{1}{ m }\)…

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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From JEE Mains

Match List \(I\) with List \(II\)

List \(I\) (molecules/ions)	List \(II\) (No. of lone pairs of \(e ^{-}\) on central atom)
\(A\) \(IF_7\)	\(I\) Three
\(B\) \(ICl^{-}_4\)	\(II\) One
\(C\) \(XeF_6\)	\(III\) Two
\(D\) \(XeF_2\)	\(IV\) Zero

Choose the correct answer from the options given below:

JEE Mains 2023 Medium

List-I (Compound)	List-II (Test)
A. Cyclohexanol	I. Hinsberg's reagent test
B. Cyclohexylamine	II. Phthalein dye test
C. Cyclohexanecarbaldehyde	III. Lucas test
D. Phenol	IV. Tollen's test

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