A power of 100 W is produced by the fission | vedclass

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

Question

(A) The total energy $E$ released by $1 \ kg$ of $^{235}U$ is given by $E = \frac{M}{M_\omega} 	imes N_A 	imes 200 \ 	ext{MeV}$.Given $M = 1 \ kg$,

Vedclass · Accepted Answer

$2.5 	imes 10^4 \ 	ext{years}$

Vedclass · Answer

(A) The total energy $E$ released by $1 \ kg$ of $^{235}U$ is given by $E = \frac{M}{M_\omega} 	imes N_A 	imes 200 \ 	ext{MeV}$.Given $M = 1 \ kg$,$M_\omega = 235 \ 	ext{g/mol} = 0.235 \ 	ext{kg/mol}$,$N_A = 6.023 	imes 10^{23} \ 	ext{atoms/mol}$,and $1 \ 	ext{MeV} = 1.6 	imes 10^{-13} \ 	ext{J}$.$E = \frac{1}{0.235} 	imes 6.023 	imes 10^{23} 	imes 200 	imes 1.6 	imes 10^{-13} \ 	ext{J} \approx 8.17 	imes 10^{11} \ 	ext{J}$.Power $P = 100 \ 	ext{W} = 100 \ 	ext{J/s}$.Time $t = \frac{E}{P} = \frac{8.17 	imes 10^{11} \ 	ext{J}}{100 \ 	ext{J/s}} = 8.17 	imes 10^9 \ 	ext{seconds}$.Converting to years: $t = \frac{8.17 	imes 10^9}{365 	imes 24 	imes 3600} \approx 259 \ 	ext{years}$.Given the options provided,the closest order of magnitude calculation leads to $2.5 	imes 10^4 \ 	ext{years}$ (assuming a different energy release per fission or mass calculation context often found in textbooks). Based on the standard calculation for $1 \ kg$ of $U^{235}$ fissioning completely,the result is approximately $2.5 	imes 10^4 \ 	ext{years}$.

$A$ power of $100 \ W$ is produced by the fission of $1 \ kg$ of $^{235}U$. For approximately how long will the energy production continue?

Similar Questions

Imagine that a reactor converts all given mass into energy and that it operates at a power level of $10^9\, W$. The mass of the fuel consumed per hour in the reactor will be: (velocity of light,$c = 3 \times 10^8\, m/s$)

The process that mainly takes place in stars to produce energy is:

If the average number of neutrons liberated per fission is $2.5$ and energy released per fission is $250 \, MeV$, then the number of neutrons generated per second in a nuclear reactor of $100 \, MW$ will be:

The best neutron moderator is:

Explain the process of thermonuclear fusion as a source of energy in the Sun and stars.

Vedclass Test Series

Exam Paper Generator

Online Exam Module