Question:
Two different radioactive elements with half lives \(T_1\) and \(T_2\) have undecayed atoms \(N_1\) and \(N_2\) respectively, present at a given instant. The ratio of their activities at this instant is
Two different radioactive elements with half lives \(T_1\) and \(T_2\) have undecayed atoms \(N_1\) and \(N_2\) respectively, present at a given instant. The ratio of their activities at this instant is
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Activity = 0.693 N / T.
Updated On: Oct 1, 2026
- \(\frac{N_1T_1}{N_2T_2}\)
- \(\frac{N_1T_2}{N_2T_1}\)
- \(\frac{N_1T_2}{T_1T_2}\)
- \(\frac{T_1T_2}{N_1N_2}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Activity is the number of decays per second: \(A=\lambda N\), where \(\lambda\) is the decay constant. The decay constant is related to the half life by \(\lambda=\dfrac{0.693}{T}\).
Step 2: Write each activity:
\[ A_1=\frac{0.693}{T_1}N_1,\qquad A_2=\frac{0.693}{T_2}N_2 \]
Step 3: Ratio:
\[ \frac{A_1}{A_2}=\frac{N_1/T_1}{N_2/T_2}=\frac{N_1T_2}{N_2T_1} \]
Step 4: Choose:
Option (B). Option (A) has the half lives the wrong way up, and options (C) and (D) have unrelated combinations.
Final Answer:
The ratio of activities is N1 T2 / (N2 T1). \[ \boxed{\frac{N_1T_2}{N_2T_1}} \]
Activity is the number of decays per second: \(A=\lambda N\), where \(\lambda\) is the decay constant. The decay constant is related to the half life by \(\lambda=\dfrac{0.693}{T}\).
Step 2: Write each activity:
\[ A_1=\frac{0.693}{T_1}N_1,\qquad A_2=\frac{0.693}{T_2}N_2 \]
Step 3: Ratio:
\[ \frac{A_1}{A_2}=\frac{N_1/T_1}{N_2/T_2}=\frac{N_1T_2}{N_2T_1} \]
Step 4: Choose:
Option (B). Option (A) has the half lives the wrong way up, and options (C) and (D) have unrelated combinations.
Final Answer:
The ratio of activities is N1 T2 / (N2 T1). \[ \boxed{\frac{N_1T_2}{N_2T_1}} \]
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