At a given instant,a radioactive sample has N | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The activity of a radioactive sample is given by $A = |dN/dt| = N\lambda$. Thus,option $A$ is correct.By definition,the decay constant $\lambda$ r

Vedclass · Accepted Answer

After a time interval of $1/\lambda$,the number of nuclei remaining in the sample is $N[1 - 1/e]$

Vedclass · Answer

(C) The activity of a radioactive sample is given by $A = |dN/dt| = N\lambda$. Thus,option $A$ is correct.By definition,the decay constant $\lambda$ represents the probability of decay per unit time for a single nucleus. Thus,option $B$ is correct.The number of nuclei remaining after time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.For $t = 1/\lambda$,the number of nuclei remaining is $N(1/\lambda) = N e^{-\lambda(1/\lambda)} = N e^{-1} = N/e$.Option $C$ states that the number of nuclei remaining is $N[1 - 1/e]$,which represents the number of nuclei that have decayed,not the number remaining. Therefore,option $C$ is incorrect.The half-life $T_{1/2}$ is given by $\ln(2)/\lambda$. Thus,option $D$ is correct.

At a given instant,a radioactive sample has $N$ active nuclei. If its decay constant is $\lambda$,which of the following relations is incorrect? (Note: $\lambda$ is very small.)

Similar Questions

Give the different units of radioactivity and define them.

If a radioactive element having a half-life of $30 \ min$ is undergoing beta decay,the fraction of the radioactive element that remains undecayed after $90 \ min$ will be:

Two radioactive materials $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion $5$ billion years ago. The other was created in a nuclear reactor $5$ minutes ago. The probability of decay during the next time interval is

$A$ radioactive substance of half-life $138.6 \text{ days}$ is placed in a box. After $n$ days, only $20\%$ of the substance is present. Then the value of $n$ is $[\ln(5) = 1.61]$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module