The half-life of Au^{198} is 2.7 , days. The | vedclass

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

Question

(B) The activity $A$ is given by $A = \lambda N$, where $\lambda = \frac{\ln 2}{T_{1/2}}$.First, convert the half-life to seconds: $T_{1/2} = 2.7 	im

Vedclass · Accepted Answer

$357$

Vedclass · Answer

(B) The activity $A$ is given by $A = \lambda N$, where $\lambda = \frac{\ln 2}{T_{1/2}}$.First, convert the half-life to seconds: $T_{1/2} = 2.7 	imes 24 	imes 3600 \, s = 233280 \, s$.The number of atoms $N$ is given by $N = \frac{m}{M} 	imes N_A = \frac{1.5 	imes 10^{-3} \, g}{198 \, g/mol} 	imes 6 	imes 10^{23} \, mol^{-1} \approx 4.545 	imes 10^{18} \, atoms$.The decay constant $\lambda = \frac{0.693}{233280 \, s} \approx 2.97 	imes 10^{-6} \, s^{-1}$.The activity $A = \lambda N = (2.97 	imes 10^{-6} \, s^{-1}) 	imes (4.545 	imes 10^{18}) \approx 1.35 	imes 10^{13} \, Bq$.Since $1 \, Ci = 3.7 	imes 10^{10} \, Bq$, the activity in Curies is $A = \frac{1.35 	imes 10^{13}}{3.7 	imes 10^{10}} \approx 365 \, Ci$.

The half-life of $Au^{198}$ is $2.7 \, days$. The activity of $1.50 \, mg$ of $Au^{198}$ if its atomic weight is $198 \, g \, mol^{-1}$ is ....... $Ci$ $(N_A = 6 \times 10^{23} \, mol^{-1})$.

Similar Questions

The half-life of a radioactive substance is $ 20 \text{ minutes} $. The time taken between $ 50\% $ decay and $ 87.5\% $ decay of the substance will be

Two radioactive samples $A_1$ and $A_2$ have decay constants $10\lambda_0$ and $\lambda_0$ respectively. If they initially contain the same number of nuclei,find the ratio of the number of undecayed nuclei after time $t = 1/(9\lambda_0)$.

The half-life of a radioactive isotope $x$ is $50$ years. It decays to another element $y$ which is stable. The two elements $x$ and $y$ were found to be in the ratio of $1 : 7$ in a sample of a given rock. The age of the rock was estimated to be ........... $years$.

Two different radioactive elements with half-lives $T_1$ and $T_2$ have undecayed atoms $N_1$ and $N_2$ respectively present at a given instant. The ratio of their activities at that instant is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module