Imagine that a reactor converts all given mass into energy and that it operates at a power level of $${10^9}watt.$$ The mass of the fuel consumed per hour in the reactor will be : (velocity of light, $$c$$ is $$3 \times {10^8}m/s$$ )
A.
$$0.96\,gm$$
B.
$$0.8\,gm$$
C.
$$4 \times {10^{ - 2}}gm$$
D.
$$6.6 \times {10^{ - 5}}gm$$
Answer :
$$4 \times {10^{ - 2}}gm$$
Solution :
Power level of reactor, $$P = \frac{E}{{\Delta t}} = \frac{{\Delta m{c^2}}}{{\Delta t}}$$
mass of the fuel consumed per hour in the reactor,
$$\frac{{\Delta m}}{{\Delta t}} = \frac{P}{{{c^2}}} = \frac{{{{10}^9}}}{{{{\left( {3 \times {{10}^8}} \right)}^2}}}kg/\sec = \frac{{3600 \times {{10}^9}}}{{9 \times {{10}^{16}}}} \times {10^3}\frac{{gm}}{{hr}}$$
Releted MCQ Question on Modern Physics >> Atoms or Nuclear Fission and Fusion
In the nuclear fusion reaction
$$_1^2H + _1^3H \to _2^4He + n$$
given that the repulsive potential energy between the two
nuclei is $$ \sim 7.7 \times {10^{ - 14}}J,$$ the temperature at which the gases must be heated to initiate the reaction is nearly
[Boltzmann’s Constant $$k = 1.38 \times {10^{ - 23}}J/K$$ ]
The binding energy per nucleon of deuteron $$\left( {_1^2H} \right)$$ and helium nucleus $$\left( {_2^4He} \right)$$ is $$1.1\,MeV$$ and $$7\,MeV$$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is