Calculate and Compare the Energy Released by A) Fusion of 1.0 Kg of Hydrogen Deep Within Sun and B) the Fission of 1.0 Kg of 235u in a Fission Reactor. - Physics


Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of 235U in a fission reactor.



(a) Amount of hydrogen, m = 1 kg = 1000 g

1 mole, i.e., 1 g of hydrogen `(""_1^1"H")`  contains 6.023 × 1023 atoms.

∴ 1000 g of `""_1^1"H"` contains 6.023 × 1023 × 1000 atoms.

Within the sun, four  `""_1^1"H"` nuclei combine and form one `""_2^4"He"` nucleus. In this process 26 MeV of energy is released.

Hence, the energy released from the fusion of 1 kg `""_1^1"H"` is:

`"E"_1 = (6.023 xx 10^23 xx 26 xx 10^3)/4`

`= 39.1495 xx 10^26 " MeV"`

(b) Amount of`""_92^235"U"` = 1 kg = 1000 g

1 mole, i.e., 235 g of  `""_92^235"U"` contains 6.023 × 1023 atoms.

∴ 1000 g of `""_92^235"U"` contains

`(6.023 xx 10^23 xx 1000)/235 "atmos"`

It is known that the amount of energy released in the fission of one atom of `""_92^235"U"` is 200 MeV.

Hence, energy released from the fission of 1 kg of `""_92^235"U"` is:

`"E"_2 = (6 xx 10^23 xx1000 xx 200)/235`

`= 5.106 xx 10^26 " MeV"`

`therefore "E"_1/"E"_1 = (39.1495 xx 10^26)/(5.106 xx 10^26) = 7.67 ~~ 8`

Therefore, the energy released in the fusion of 1 kg of hydrogen is nearly 8 times the energy released in the fission of 1 kg of uranium.

Concept: Nuclear Energy - Nuclear Fission
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Chapter 13: Nuclei - Exercise [Page 466]


NCERT Physics Class 12
Chapter 13 Nuclei
Exercise | Q 13.30 | Page 466
NCERT Physics Class 12
Chapter 13 Nuclei
Exercise | Q 30 | Page 466


Suppose, we think of fission of a `""_26^56"Fe"` nucleus into two equal fragments `""_13^28"Al"`. Is the fission energetically possible? Argue by working out Q of the process. Given  `"m"(""_26^56 "Fe") = 55.93494 "u"`  and `"m"(""_13^28 "Al") = 27.98191 "u"`.

Suppose India had a target of producing by 2020 AD, 200,000 MW of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was 25%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of 235U to be about 200MeV.

In a typical fission reaction, the nucleus is split into two middle-weight nuclei of unequal masses. Which of the two (heavier or lighter) has greater kinetic energy? Which one has greater liner momentum? 

If three helium nuclei combine to form a carbon nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimise the energy?

The mass of a neutral carbon atom in ground state is

As compared to 12C atom, 14C atom has

The heavier nuclei tend to have larger N/Z ratio because
(a) a neutron is heavier than a proton
(b) a neutron is an unstable particle
(c) a neutron does not exert electric repulsion
(d) Coulomb forces have longer range compared to the nuclear forces.

As the mass number A increases, which of the following quantities related to a nucleus do not change?

A free neutron decays to a proton but a free proton does not decay to a neutron. This is because

Calculate the energy released by 1g of natural uranium assuming 200 MeV is released in each fission event and that the fissionable isotope 235U has an abundance of 0.7% by weight in natural uranium.

A uranium reactor develops thermal energy at a rate of 300 MW. Calculate the amount of 235U being consumed every second. Average released per fission is 200 MeV.

Calculate the Q-value of the fusion reaction 4He + 4He = 8Be. Is such a fusion energetically favourable? Atomic mass of 8Be is 8.0053 u and that of 4He is 4.0026 u.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Calculate the energy that can be obtained from 1 kg of water through the fusion reaction 2H + 2H → 3H + p. Assume that 1.5 × 10−2% of natural water is heavy water D2O (by number of molecules) and all the deuterium is used for fusion.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

A town has a population of 1 million. The average electric power needed per person is 300 W. A reactor is to be designed to supply power to this town. The efficiency with which thermal power is converted into electric power is aimed at 25%. (a) Assuming 200 MeV to thermal energy to come from each fission event on an average, find the number of events that should take place every day. (b) Assuming the fission to take place largely through 235U, at what rate will the amount of 235U decrease? Express your answer in kg per day. (c) Assuming that uranium enriched to 3% in 235U will be used, how much uranium is needed per month (30 days)?

Which particle is most likely to be captured by a 235u nucleus and cause it to undergo fission? 

Assuming that about 200 MeV of energy is released per fission of 92U235 nuclei, then the mass of U235 consumed per day in a fission reactor of power 1 megawatt will be approximately ______.

A heavy nucleus P of mass number 240 and binding energy of 7.6 MeV per nucleon splits into two nuclei Q and R of mass number 110 and 130 and binding energy per nucleon of 8.5 MeV and 8.4 MeV respectively. Calculate the energy released in fission.


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