JEE Mains · Physics · STD 12 - 13. Nuclei

The half-life of \(Au ^{198}\) is \(2.7\, days.\) The activity of \(1.50\, mg\) of \(Au ^{198}\) if its atomic weight is \(198\, g mol ^{-1}\) is .......\(Ci\) \(\left( N _{ A }=6 \times 10^{23}\, / mol \right)\)

A \(240\)
B \(357\)
C \(535\)
D \(252\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(357\)

Step-by-step Solution

Detailed explanation

\(A =\lambda N\) \(N = nN _{ A }\)\(\quad\left( t _{1 / 2}=\frac{\ln 2}{\lambda}\right)\) \(N =\left(\frac{1.5 \times 10^{-3}}{198}\right) N _{ A }\) \(A=\left(\frac{\ln 2}{t_{1 / 2}}\right) N\) \(1\) Curie \(=3.7 \times 10^{10}\, Bq\) \(A =365\, Bq\)

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.

Same subject

Match the List\(-I\) with List\(-II\).

List \(I\)	List \(II\)
\(A\) \(AC\) generator	\(I\) Presence of both \(L\) and \(C\)
\(B\) Transformer	\(II\) Electromagnetic Induction
\(C\)Resonance phenomenon to occur	\(III\) Quality factor
\(D\)Sharpness of resonance	\(IV\) Mutual Inductance

Choose the correct answer from the options given below:

JEE Mains 2023 Medium

Explore more questions on app

From JEE Mains

Explore more questions on app

List - I	List - II
A. AM Broadcast	I. \(88-108 MHz\)
B. FM Broadcast	II. \(540-1600 kHz\)
C. Television	III. \(3.7-4.2GHz\)
D. Satellite Communication	IV. \(54 MHz-590MHz\)