A nuclear power plant supplying electrical po | vedclass

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

Question

(C) The power generated by the nuclear plant is directly proportional to the activity $A$ of the radioactive fuel. Let $P_0$ be the initial power and

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The power generated by the nuclear plant is directly proportional to the activity $A$ of the radioactive fuel. Let $P_0$ be the initial power and $P(t)$ be the power at time $t$.The activity at time $t$ is given by $A(t) = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}$,where $T$ is the half-life.Given that the village's power requirement $P_{req}$ is $12.5 \%$ of the initial power $P_0$,we have $P_{req} = 0.125 P_0 = \frac{1}{8} P_0$.The plant can meet the needs as long as $P(t) \ge P_{req}$. The maximum time $t = nT$ occurs when $P(nT) = P_{req}$.Thus,$P_0 \left(\frac{1}{2}\right)^{\frac{nT}{T}} = \frac{1}{8} P_0$.$\left(\frac{1}{2}\right)^n = \frac{1}{8} = \left(\frac{1}{2}\right)^3$.Comparing the exponents,we get $n = 3$.

Similar Questions

What fraction of a radioactive material will get disintegrated in a period of two half-lives?

$A$ 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 ......... $\%$

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 $= 6.023 \times 10^{23}$).

The half-life of a radioactive substance is $20 \ min$. The time interval between $20\%$ decay and $80\%$ decay is ......... $min$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module