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

The energy released in an atom bomb is obtained from?

If the number of uranium nuclei required per hour to produce a power of $64 \text{ kW}$ is $7.2 \times 10^{18}$,then the energy released per fission is

The binding energy of deuteron is $2.2 \, MeV$ and that of $_2^4He$ is $28 \, MeV$. If two deuterons are fused to form one $_2^4He$,then the energy released is ......... $MeV$.

$200\, MeV$ of energy may be obtained per fission of ${U^{235}}$. $A$ reactor is generating $1000\, kW$ of power. The rate of nuclear fission in the reactor is

The scientific principle that forms the basis of the Tokamak technology is

Vedclass Test Series

Exam Paper Generator

Online Exam Module