Half-lives of two radioactive nuclei A and B | vedclass

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

Question

(A) Let the initial number of nuclei be $N_0$ for both $A$ and $B$. For nucleus $A$,half-life $T_{1/2, A} = 10 \, min$. After $t = 60 \, min$,the numb

Vedclass · Accepted Answer

$9 : 8$

Vedclass · Answer

(A) Let the initial number of nuclei be $N_0$ for both $A$ and $B$. For nucleus $A$,half-life $T_{1/2, A} = 10 \, min$. After $t = 60 \, min$,the number of half-lives $n_A = 60/10 = 6$. The number of undecayed nuclei $N_A = N_0 / 2^6 = N_0 / 64$. The number of decayed nuclei $D_A = N_0 - N_A = N_0(1 - 1/64) = 63N_0 / 64$. For nucleus $B$,half-life $T_{1/2, B} = 20 \, min$. After $t = 60 \, min$,the number of half-lives $n_B = 60/20 = 3$. The number of undecayed nuclei $N_B = N_0 / 2^3 = N_0 / 8$. The number of decayed nuclei $D_B = N_0 - N_B = N_0(1 - 1/8) = 7N_0 / 8$. The ratio of decayed nuclei $D_A / D_B = (63N_0 / 64) / (7N_0 / 8) = (63/64) 	imes (8/7) = 9/8$.

Half-lives of two radioactive nuclei $A$ and $B$ are $10 \, minutes$ and $20 \, minutes$,respectively. If,initially,a sample has an equal number of nuclei,then after $60 \, minutes$,the ratio of the number of decayed nuclei of $A$ and $B$ will be:

Similar Questions

$A$ radioactive sample has a half-life of $5$ years. The percentage of the fraction decayed in $10$ years will be (in $\%$)

The half-life of the radioisotope tritium $(_1^3H)$ is $12.3$ years. If the initial amount of tritium is $32 \ mg$, how much amount (in $mg$) will remain after $49.2$ years?

$A$ 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 $[\ln(5) = 1.61]$.

$A$ heavy nucleus $Q$ of half-life $20 \text{ minutes}$ undergoes alpha-decay with a probability of $60 \%$ and beta-decay with a probability of $40 \%$. Initially,the number of $Q$ nuclei is $1000$. The number of alpha-decays of $Q$ in the first one hour is:

$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?

Vedclass Test Series

Exam Paper Generator

Online Exam Module