Sigma Percentile
JEE Advanced 2009
LEVELJEE Advanced

Animated Solution for Physics - Atoms and Nuclei: Comprehension Passage

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, known as deuteron and denoted by D can be thought of as a candidate for fusion reactor. The D-D reaction is . In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time before the particles fly away from the core. If is the density (number/volume) of deuterons, the product is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than . It may be helpful to use the following : Boltzmann constant ; .
Question 1:

In the core of nuclear fusion reactor, the gas becomes plasma because of

Select Answer:

Question 2:

Assume that two deuteron nuclei in the core of fusion reactor at temperature are moving towards each other, each with kinetic energy , when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature required for them to reach a separation of is in the range

Select Answer:

Question 3:

Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion ?

Select Answer:

Visualized Solution

The Sigma Insight: Nucleus and Nuclear Reaction

Solution Diagram
The journey into the heart of a nuclear fusion reactor is nothing short of fascinating. Let's break down the physics behind this incredible process step-by-step, addressing each of the three questions based on the passage.

The Birth of Plasma

Our first question asks why the gas in the reactor core becomes plasma. To understand this, we need to look at the conditions required for nuclear fusion. Fusion involves bringing positively charged nuclei so close together that the strong nuclear force takes over. However, these nuclei naturally repel each other due to the electrostatic Coulomb force.
To overcome this massive repulsion, the particles must be moving at incredibly high speeds. How do we achieve such speeds? By raising the temperature to astronomical levels! At these extreme temperatures, the thermal energy is so intense that atoms are completely stripped of their electrons. The gas becomes a soup of free-roaming nuclei and electrons—a state of matter known as plasma. Therefore, the gas becomes plasma because of the high temperature maintained inside the reactor core.

The Dance of the Deuterons

Next, let's calculate the temperature required for two deuterons to reach a specific separation distance. Imagine two deuterons hurtling towards each other. Initially, they are far apart, so their electrostatic potential energy is effectively zero. Each deuteron has a kinetic energy of , making the total initial kinetic energy:
As they approach each other, the repulsive Coulomb force slows them down. At their distance of closest approach (), they momentarily come to a halt. All their kinetic energy has been converted into electrostatic potential energy. By the principle of conservation of mechanical energy:
Now, we substitute the given values into our master equation:
Let's simplify the right side:
This calculated temperature falls perfectly within the range .

The Lawson Criterion

Finally, we evaluate the four reactor designs based on the Lawson criterion. For a fusion reactor to be successful and produce net positive energy, the product of the deuteron density () and the confinement time () must exceed a specific threshold:
Let's test the most promising candidate, option (b):
Since is strictly greater than , this design satisfies the Lawson criterion and is the most promising among the choices!

Similar Questions

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In the nuclear fusion reaction, given that the repulsive potential energy between the two nuclei is J, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant, J/K]

(A)
K
(B)
K
(C)
K
(D)
K
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Consider the reaction : . Mass of the deuterium atom = 2.0141 u. Mass of helium atom = 4.0024 u. This is a nuclear ........ reaction in which the energy released is ...... MeV.

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The binding energy per nucleon of deuteron () and helium nucleus () is and respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

(A)
(B)
(C)
(D)
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It is proposed to use the nuclear fusion reaction; in a nuclear reactor of rating. If the energy from the above reaction is used with a per cent efficiency in the reactor, how many grams of deuterium fuel will be needed per day? (The masses of and are atomic mass units and atomic mass units respectively.)

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The binding energies per nucleon for deuteron () and helium () are and respectively. The energy released when two deuterons fuse to form a helium nucleus () is ......... .

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A star initially has deuterons. It produces energy via the processes and . If the average power radiated by the star is W, the deuteron supply of the star is exhausted in a time of the order of The mass of the nuclei are as follows: ; ; ; .

(A)
s
(B)
s
(C)
s
(D)
s
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From the following equations pick out the possible nuclear fusion reactions

* Multiple Correct Options
(A)
(B)
(C)
(D)
JEE Advanced 2015
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A fission reaction is given by , where and are two particles. Considering to be at rest, the kinetic energies of the products are denoted by , , (2 MeV) and (2 MeV), respectively. Let the binding energies per nucleon of , and be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct options is/are

* Multiple Correct Options
(A)
, , ,
(B)
, , ,
(C)
, , ,
(D)
, , ,
JEE Main 2022
LEVELJEE Advanced

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction in a laboratory frame is (in ). Assume that is at rest in the laboratory frame. The masses of , , and can be taken to be , , and , respectively, where . The value of is_________.

JEE Advanced 2013
LEVELJEE Advanced

Comprehension Passage

The mass of a nucleus is less than the sum of the masses of number of neutrons and number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass can break into two light nuclei of masses and only if . Also two light nuclei of masses and can undergo complete fusion and form a heavy nucleus of mass only if . The masses of some neutral atoms are given in the table below: $\begin{array}{llll} _{1}^{1}\text{H} & 1.007825\text{u} & _{1}^{2}\text{H} & 2.014102\text{u} \\ _{3}^{6}\text{Li} & 6.01513\text{u} & _{3}^{7}\text{Li} & 7.016004\text{u} \\ _{64}^{152}\text{Gd} & 151.919803\text{u} & _{82}^{206}\text{Pb} & 205.974455\text{u} \\ _{1}^{3}\text{H} & 3.016050\text{u} & _{2}^{4}\text{He} & 4.002603\text{u} \\ _{30}^{70}\text{Zn} & 69.925325\text{u} & _{34}^{82}\text{Se} & 81.916709\text{u} \\ _{84}^{210}\text{Po} & 209.982876\text{u} & & \end{array}$
Question 1:

The correct statement is

(A)
The nucleus can emit an alpha particle.
(B)
The nucleus can emit a proton.
(C)
Deuteron and alpha particle can undergo complete fusion.
(D)
The nuclei and can undergo complete fusion.
Question 2:

The kinetic energy (in keV) of the alpha particle, when the nucleus at rest undergoes alpha decay, is

(A)
5316
(B)
5422
(C)
5707
(D)
5818