KCET · Physics · Atomic Physics
The relation between half life \( (T) \) and decay constant \( (\lambda) \) is
- A \( \lambda T=1 \)
- B \( \lambda T=\frac{1}{2} \)
- C \( \lambda T=\log _{e} 2 \)
- D \( \lambda=\log 2 T \)
Answer & Solution
Correct Answer
(C) \( \lambda T=\log _{e} 2 \)
Step-by-step Solution
Detailed explanation
Relation between half-life \((\mathrm{T})\) and decay constant \((\lambda)\) is
\(T=\frac{0.693}{\lambda}\)
\(\Rightarrow \lambda T=0.693\)
Therefore, \(\lambda T=\log _{e} 2\)
\(T=\frac{0.693}{\lambda}\)
\(\Rightarrow \lambda T=0.693\)
Therefore, \(\lambda T=\log _{e} 2\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A current of \(5 \mathrm{~A}\) is passing through a metallic wire of cross-sectional area \(4 \times 10^{-6} \mathrm{~m}^{2}\) If the density of charge carriers of the wire is \(5 \times 10^{26} \mathrm{~m}^{-3}\) the drift velocity of the electronswill beKCET 2007 Easy
- The resistance \( \mathrm{R}=\frac{V}{I} \) where \( \mathrm{V}=(100 \pm 5) \mathrm{V} \) and \( \mathrm{I}=(10 \pm 0.2) \mathrm{A} . \) The percentage error in \( \mathrm{R} \)
isKCET 2018 Easy - There is a uniform electric field of intensity E which is as shown. How many labelled points have the same electric potential as the fully shaded point?
KCET 2010 Easy - To get an output \(Y=1\) from the circuit shown, the inputs and must be respectively
KCET 2008 Easy - The velocity of a particle moving along \(x\)-axis is given as \(V = x^2 - 5x + 4\) (in m/s) where \(x\) denotes the \(x\)-coordinate of the particle in metres. The magnitude of the acceleration of the particle when the velocity of the particle zero isKCET 2026 Medium
- Young's modulus of a perfect rigid body isKCET 2020 Easy
More PYQs from KCET
- The correct equation depicting species-area relationship isKCET 2021 Medium
- Which of the following aqueous solution has highest freezing point?KCET 2017 Hard
- Which of these is NOT a method host cells 'competent' to take up DNA?KCET 2023 Hard
- The following is a scheme showing the electron transport system. Identify the electron carrier molecules indicated as A and B. Choose the correct option,
KCET 2010 Easy - A carnot engine takes \( 300 \) calories of heat from a source at \( 500 \mathrm{~K} \) and rejects \( 150 \) calories of
heat to the sink. The temperature of the sink isKCET 2018 Easy - The s-block element used as a catalyst in the manufacture of Buna-S rubber isKCET 2012 Easy