Yes
In high temperature gas cooled nuclear fission reactors using the nuclear process heat.
Both processes change the nature of the atom.
Nuclear fission happens spontaneously in nature. Uranium-235 does this, and is the only commonly occurring natural isotope that does. Nuclear fission can be induced by crashing a neutron into a fissionable atom. Some things other than Uranium-235 are fissionable, notably Uranium-238. Fission has been induced in various experiments. It happens in nuclear reactors and in nuclear bombs.
Fission is not a natural process in the sense that it typically does not occur spontaneously in nature. Fission reactions are artificially induced and controlled in nuclear reactors to produce energy. However, fission can occur as a natural process in some rare scenarios, such as in certain isotopes of uranium found in nature.
The formula for a nuclear bomb involves the process of nuclear fission or fusion. In the case of fission bombs, such as the atomic bombs dropped on Hiroshima and Nagasaki, the formula involves the splitting of heavy atomic nuclei like uranium or plutonium. For fusion bombs, like thermonuclear weapons, the formula involves the fusion of light atomic nuclei like hydrogen isotopes. The specific details and equations involved are complex and highly classified due to the sensitive nature of nuclear weapons technology.
Uranium-238 and Uranium-235 do not release neutrons spontaneously in nature in the same way they do during a fission process. Neutrons are typically required to initiate the fission process in nuclear reactions. In natural settings, radioactive decay processes such as alpha and beta decay occur in uranium isotopes, but not neutron release.
In a nuclear chain reaction, neutrons for nuclear fission primarily come from the fission of heavy atomic nuclei, such as uranium-235 or plutonium-239. When these nuclei absorb a neutron and become unstable, they split into smaller nuclei, releasing additional neutrons in the process. These emitted neutrons can then initiate further fission reactions in nearby nuclei, sustaining the chain reaction. Thus, the process relies on the self-propagating nature of neutron release and absorption.
first it occur in nature and second it occur in power plant
In a nuclear power plant and in nature in (low levels.) With any form of radioactive decay it is possible for atoms to be split. The sustained reaction is the foundation of both nuclear weapons and nuclear power plants where the fission is self-sustaining for a period of time. A simple physical model is a pool (billard) table when you initally break. The cue ball is a small particle that breaks up the racked balls. Now imagine hundreds if not millions of other racked balls. A chain reaction of breaks continues until there isn't enough energy to stustain the fission of atoms. Low levels of this happen all the time with radioactive material in nature. Once there is a "critical mass" of very specific radioactive material a sustained chain reaction happens. Controlled you can get nuclear power by siphoning the reaction in the form of heat to turn turbines for power, let it all go at once and you get a nuclear bomb. Fission is the splitting of atoms, fusion is merging atoms. A hydrogen bomb uses both fission and fusion. Fission to start the reaction (Plutonium) and an outer shell that (Cesium,cobalt, if memory serves me correctly were two material used for the outer casing), from the force of the fission, causes the fusion of hyrodgen (hence H-Bomb).
Transmutation is the process by which one element changes into another. This can only be done with a nuclear reaction, but alchemists once believed it might be possible, for example, to transmute lead into gold. They tried many bizarre things, but were never successful. Only nuclear reactions, such as fusion, fission, radioactive decay, etc, can induce a transmutation
Plutonium-239 is not found in nature in significant quantities and is primarily produced in nuclear reactors as a byproduct of nuclear fission reactions. It is a man-made element that is typically created for use in nuclear weapons and reactor fuel.
Hydrogen-3, also known as tritium, is a rare and radioactive isotope of hydrogen that is not commonly found in nature. It is primarily produced artificially in nuclear reactors and particle accelerators.
Oklo in Africa when the natural concentration of Uranium-235 was near 5% instead of the current 0.7%. This was about 3 billion years ago.