If 20 , g of a radioactive substance reduces | vedclass

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

Question

(B) The half-life $T_{1/2}$ is the time taken for a substance to reduce to half its initial mass.Given that $20 \, g$ reduces to $10 \, g$ in $4 \, mi

Vedclass · Accepted Answer

In $12 \, minutes$

Vedclass · Answer

(B) The half-life $T_{1/2}$ is the time taken for a substance to reduce to half its initial mass.Given that $20 \, g$ reduces to $10 \, g$ in $4 \, minutes$, the half-life $T_{1/2} = 4 \, minutes$.We use the radioactive decay formula: $M = M_0 \left( \frac{1}{2} \right)^{t / T_{1/2}}$, where $M$ is the final mass, $M_0$ is the initial mass, and $t$ is the time elapsed.Substituting the values $M = 10 \, g$, $M_0 = 80 \, g$, and $T_{1/2} = 4 \, minutes$:$10 = 80 \left( \frac{1}{2} \right)^{t / 4}$$\frac{10}{80} = \left( \frac{1}{2} \right)^{t / 4}$$\frac{1}{8} = \left( \frac{1}{2} \right)^{t / 4}$Since $\frac{1}{8} = \left( \frac{1}{2} \right)^3$, we have:$\left( \frac{1}{2} \right)^3 = \left( \frac{1}{2} \right)^{t / 4}$Equating the exponents: $3 = \frac{t}{4}$$t = 12 \, minutes$.

If $20 \, g$ of a radioactive substance reduces to $10 \, g$ due to radioactive decay in $4 \, minutes$, then in what time will $80 \, g$ of the same substance reduce to $10 \, g$?

Similar Questions

The half-life of a radioactive substance against $\alpha$-decay is $1.2 \times 10^7 \, s$. What is the decay rate for $4.0 \times 10^{15}$ atoms of the substance?

The half-life of $^{215}At$ is $100 \,\mu s$. After how much time (in $\mu s$) will $1/16^{th}$ of the sample remain undecayed?

If the half-life of radium is $77$ days,its decay constant in $day^{-1}$ will be:

The activity of a radioactive material is $2.56 \times 10^{-3} \, Ci$. If the half-life of the material is $5 \, \text{days}$, after how many days will the activity become $2 \times 10^{-5} \, Ci$?

In a fossil bone,the ratio of $^{14}C : ^{12}C$ is $1/16$ of the ratio found in a living animal. If the half-life of $^{14}C$ is $5730 \text{ years}$,find the age of the fossil bone in years.

Vedclass Test Series

Exam Paper Generator

Online Exam Module