LEVELJEE Main
Visualized Solution
The Sigma Insight: Nucleus and Nuclear Reaction
The Challenge of Nuclear Fusion
Imagine you are trying to push two extremely powerful magnets together by their north poles. The closer they get, the harder they push back. This is exactly what happens in a nuclear fusion reaction. We are trying to fuse two positively charged nuclei—in this case, Deuterium () and Tritium (). Because they both carry a positive charge, they experience a tremendous electrostatic repulsive force, often called the Coulomb barrier.
To make them fuse, we have to throw them at each other with enough kinetic energy to overcome this repulsive potential energy. But how do we give atomic nuclei that much energy? We heat them up!
The Master Equation
Kinetic Theory Meets Nuclear Physics
According to the Kinetic Theory of Gases, the average translational kinetic energy of a particle in a gas at an absolute temperature is given by:
where is the Boltzmann constant ().
For the fusion reaction to initiate, this average thermal kinetic energy must be at least equal to the repulsive potential energy between the two nuclei. The problem states that this repulsive potential energy is .
So, we set up our master equation by equating the two energies:
Final Calculation
Now, let's substitute the given values into our equation. I know this looks like a lot of scientific notation, but let's take a breath and solve it step-by-step.
To isolate the temperature , we cross-multiply the and divide by and the Boltzmann constant:
When we compute this fraction, the powers of simplify to (since ). Dividing by gives us approximately .
This is an astronomically high temperature—literally the temperature found in the cores of stars! Looking at our options, the closest order of magnitude is . This beautifully illustrates why achieving controlled nuclear fusion on Earth requires such extreme conditions.
Similar Questions
JEE Advanced 2009
LEVELJEE Advanced
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
(A)
strong nuclear force acting between the deuterons.
(B)
Coulomb force acting between the deuterons.
(C)
Coulomb force acting between deuteron-electron pairs.
(D)
the high temperature maintained inside the reactor core.
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
(A)
(B)
(C)
(D)
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 ?
(A)
Deuteron density , confinement time
(B)
Deuteron density , confinement time
(C)
Deuteron density , confinement time
(D)
Deuteron density , confinement time
LEVELJEE Main
From the following equations pick out the possible nuclear fusion reactions
* 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_________.
LEVELJEE Main
If the binding energy per nucleon in and nuclei are and respectively, then in the reaction energy of proton must be
(A)
(B)
(C)
(D)
LEVELJEE Main
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)
LEVELJEE Main
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 ......... .
LEVELJEE Main
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.
LEVELBoard
During a nuclear fusion reaction
(A)
a heavy nucleus breaks into two fragments by itself
(B)
a light nucleus bombarded by thermal neutrons breaks up
(C)
a heavy nucleus bombarded by thermal neutrons breaks up
(D)
two light nuclei combine to give a heavier nucleus and possibly other products
JEE Main 2020
LEVELJEE Advanced
In a reactor, of fuel is fully used up in . The energy released per fission is . Given that, the Avogadro number, and . The power output of the reactor is close to
(A)
(B)
(C)
(D)
JEE Advanced 2006
LEVELJEE Main