The relation between $\lambda $ and $({T_{1/2}})$ is (${T_{1/2}}=$ half life, $\lambda=$ decay constant)
The relation between $\lambda $ and $({T_{1/2}})$ is (${T_{1/2}}=$ half life, $\lambda=$ decay constant)
- [AIPMT 2000]
- A
$\left(\lambda+ T _{1 / 2}\right)=\frac{ln }{2}$
- B
$T _{1 / 2}=\frac{ln2}{\lambda}$
- C
$T _{1 / 2}\; ln 2=\lambda$
- D
$T _{1 / 2}=\frac{1}{\lambda}$
Similar Questions
$x$ fraction of a radioactive sample decay in $t$ time. How much fraction will decay in $2t$ time
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Write the definition of half life of radioactive substance and obtain its relation to decay constant.
Write the definition of half life of radioactive substance and obtain its relation to decay constant.
Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes, the ratio of remaining number of $A$ and $B$ nuclei is
Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes, the ratio of remaining number of $A$ and $B$ nuclei is
- [AIPMT 1998]
Given below are two statements :
Statement $I:$ The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.
Statement $II:$ The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time $t =0$.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements :
Statement $I:$ The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.
Statement $II:$ The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time $t =0$.
In the light of the above statements, choose the most appropriate answer from the options given below :
- [NEET 2022]
Two radioactive materials $X_1$ and $X_2$ have decay constant $5\lambda$ and $\lambda$ respectively intially they have the saame number of nuclei, then the ratio of the number of nuclei of $X_1$ to that $X_2$ will be $\frac{1}{e}$ after a time
Two radioactive materials $X_1$ and $X_2$ have decay constant $5\lambda$ and $\lambda$ respectively intially they have the saame number of nuclei, then the ratio of the number of nuclei of $X_1$ to that $X_2$ will be $\frac{1}{e}$ after a time
- [AIPMT 2008]