I would like to know why scientists try to use deuterium and tritium for fusion and not just the ordinary isotope of Hydrogen ${}^1H$?
[Physics] Fusion: Why deuterium and tritium
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While D-He3 fusion reaction rate peaks at smaller energies than D-D (see this picture), and produce more energy (18MeV for D-He3 vs. 3-4MeV for D-D reaction), this is not the main reason why some people think He3 is a 'better' fuel. The main reason is that D-He3 fusion fuel cycle is aneutronic. That is, all fusion products (if we disregard auxiliary branches) are charged particles and there are no neutrons released in this reaction.
For more information read corresponding wiki page, but the main reasons neutrons are considered 'bad' in fusion are following:
energetic neutrons require considerable shielding (there are no other way to stop them other than slow them down in matter and then absorb).
neutrons cause material activation, producing radioactive waste.
if large portion of fusion energy is released with neutrons, this means that electricity has to be produced through thermal conversion (steam turbines with relatively low efficiency). On the other hand, if all energy released as a charged fusion products, then the electricity could be produced by direct conversion with potentially much higher efficiency and much smaller devices.
Additionally, one half of D-D reactions produces radioactive tritium that either has to be 'burned', or stored.
All of this would be especially crucial in space, where shielding + turbines + radiators for excess heat will make D-D fuel less attractive then D-He3 if there is sufficient space industry to make He3 mining viable.
For an efficient fusion reaction, you need to get more energy out than you put in. The fusion of hydrogen gives off more energy, once you can manage to control and compress it, (which is the difficult part), than the energy input involved in "squeezing" the particles together.
Once you achieve that goal, you obtain a net energy gain.
An indication of the problems inherent in controlled nuclear is illustrated by this comment from David Hammen.
Controlled nuclear fusion employs temperatures much greater than those at the center of the Sun, but at a vastly decreased pressure compared to the center of the Sun. Controlled fusion also bypasses the initial proton-proton fusion step, which is the bottleneck in fusion in a one solar mass star. This bottleneck is why even though it is 4.6 billion years old, the Sun has consumed less than half of the hydrogen in the core.
Image Source: Wikipedia Nuclear Binding Energies
On this chart, you can get some idea of the forces we would have to overcome to utilise other elements in fusion reactions, and you might notice it flattens out at iron.
I would like to have a scientific answer why possibly any other material is not considering for fusion reactor? However, is there any theoretical possibilities of using other matter, e.g. using Hg?
With other elements, the ratio of energy in to energy out is much less, so they are not as efficient. In fact when you go up the periodic table as far as iron, you won't get any more out by fusing them together. That's part of the reason we are here today. Stars transmute elements, starting with hydrogen up as far as iron, then because there is no net energy output the star explodes from the pressure from gravity on the outside, which the star is incapable of resisting without having core energy emerging from fusion reactions.
Best Answer
The problem with attempting to fuse two protons is that there is no bound state $^2$He, for the rather obvious reason that there are no neutrons present to hold the two protons together. The fusion of two protons requires one of them to undergo beta plus decay while the two protons are close, and the probability of this is vanishingly small. It happens in the Sun because there are an awful lot of proton collisions in the Sun's core and even the tiny probability of fusion produces a sizable overall reaction rate.
By contrast fusing deuterium and tritium produces $^5$He, which does have a bound state, so this has a relatively large probability. The deuterium and tritium fuse to form $^5$He, and this then decays to $^4$He and a neutron with a half life of about $7 \times 10^{-22}$ seconds.
See the related question: How much faster is the fusion we make on earth compared to the fusion that happens in the sun?