A certain radioactive substance has a half-li | vedclass

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

Question

(B) The half-life of the radioactive substance is $T_{1/2} = 5\, years$.The total time elapsed is $t = 10\, years$.The number of half-lives passed is

Vedclass · Accepted Answer

$75$

Vedclass · Answer

(B) The half-life of the radioactive substance is $T_{1/2} = 5\, years$.The total time elapsed is $t = 10\, years$.The number of half-lives passed is $n = t / T_{1/2} = 10 / 5 = 2$.The fraction of undecayed nuclei remaining after $n$ half-lives is given by $N/N_0 = (1/2)^n$.Substituting $n = 2$, we get $N/N_0 = (1/2)^2 = 1/4$.This means $1/4$ of the original nuclei remain undecayed.The fraction of nuclei that have decayed is $1 - N/N_0 = 1 - 1/4 = 3/4$.To express this as a percentage, we multiply by $100$: $(3/4) 	imes 100\% = 75\%$.Therefore, the probability of decay for a nucleus in $10\, years$ is $75\%$.

$A$ certain radioactive substance has a half-life of $5\, years$. Thus, for a nucleus in a sample of the element, the probability of decay in $10\, years$ is ......... $\%$

Similar Questions

Give the equation form of the exponential law of radioactive decay.

The decay constant $\lambda$ of a radioactive sample is the probability of decay of an atom in unit time. Then,

$A$ sample of a radioactive element contains $8 \times 10^{16}$ active nuclei. The half-life of the element is $15 \text{ days}$. The number of nuclei decayed after $60 \text{ days}$ is:

The half-life of $^{238}_{92}U$ undergoing $\alpha$-decay is $4.5 \times 10^{9} \text{ years}$. What is the activity of a $1 \text{ g}$ sample of $^{238}_{92}U$?

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module