The half-lives of two radioactive materials A | vedclass

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

Question

(A) The mass of a radioactive substance remaining after time $t$ is given by $M = M_0 (1/2)^{t/T_{1/2}}$, where $M_0$ is the initial mass and $T_{1/2}

Vedclass · Accepted Answer

$2T$

Vedclass · Answer

(A) The mass of a radioactive substance remaining after time $t$ is given by $M = M_0 (1/2)^{t/T_{1/2}}$, where $M_0$ is the initial mass and $T_{1/2}$ is the half-life.For material $A$: $M_A = M_{0A} (1/2)^{t/T}$.For material $B$: $M_B = M_{0B} (1/2)^{t/2T}$.Given the ratio of initial masses $M_{0A} / M_{0B} = 8/1$ and the ratio of remaining masses $M_A / M_B = 4/1$.Therefore, $\frac{M_A}{M_B} = \frac{M_{0A}}{M_{0B}} \cdot \frac{(1/2)^{t/T}}{(1/2)^{t/2T}} = 4/1$.Substituting the values: $8 \cdot (1/2)^{t/T - t/2T} = 4$.$8 \cdot (1/2)^{t/2T} = 4$.$(1/2)^{t/2T} = 4/8 = 1/2$.$(1/2)^{t/2T} = (1/2)^1$.Comparing the exponents, $t/2T = 1$, which gives $t = 2T$.

The half-lives of two radioactive materials $A$ and $B$ are $T$ and $2T$ respectively. If the ratio of the initial masses of the materials $A$ and $B$ is $8:1$, then the time after which the ratio of the masses of the materials $A$ and $B$ becomes $4:1$ is

Similar Questions

In a radioactive sample,there are $1.414 \times 10^6$ active nuclei. If they reduce to $10^6$ within $10 \text{ min}$,then the half-life of this sample will be ....... $\text{min}$.

$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source is .......... $min$.

Half-lives for $\alpha$ and $\beta$ emission of a radioactive material are $16$ years and $48$ years respectively. When the material decays by giving $\alpha$ and $\beta$ emission simultaneously,the time in which $3/4$th of the material decays is ....... years.

If $f$ denotes the ratio of the number of nuclei decayed $(N_{d})$ to the number of nuclei at $t=0$ $(N_{0})$,then for a collection of radioactive nuclei,the rate of change of $f$ with respect to time is given as: [$\lambda$ is the radioactive decay constant]

The half-life of a radioactive nuclide is $100 \, hours$. The fraction of original activity that will remain after $150 \, hours$ would be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module