Question:
The dimensional formula for the product of the decay constant \(\lambda\) and the mean life of a radioactive substance is
The dimensional formula for the product of the decay constant \(\lambda\) and the mean life of a radioactive substance is
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If units cancel out completely, the quantity is dimensionless.
Updated On: Apr 24, 2026
- \(LMT^2\)
- \(L^0MT^{-2}\)
- \(LMT\)
- \(L^0M^0T^0\)
- \(L^2M^2T^2\)
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The Correct Option is D
Solution and Explanation
Concept:
• Decay constant \( \lambda \) has dimension \(T^{-1}\)
• Mean life \( \tau = \frac{1}{\lambda} \) has dimension \(T\)
Step 1: Multiply quantities.
\[ \lambda \times \tau = T^{-1} \times T = 1 \]
Step 2: Dimension.
Dimensionless quantity: \[ L^0 M^0 T^0 \]
• Decay constant \( \lambda \) has dimension \(T^{-1}\)
• Mean life \( \tau = \frac{1}{\lambda} \) has dimension \(T\)
Step 1: Multiply quantities.
\[ \lambda \times \tau = T^{-1} \times T = 1 \]
Step 2: Dimension.
Dimensionless quantity: \[ L^0 M^0 T^0 \]
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