Nuclear energy is related to nonrenewable and/or non-conventional primary energy sources.
nuclear power
Nuclear energy is a form unto itself. But please see the related question linked below.
Atomic energy is related to the process of nuclear fission or fusion, where energy is released by splitting or combining atomic nuclei. This energy can be harnessed for power generation in nuclear reactors, for medical applications such as cancer treatment using radiation therapy, and in nuclear weapons.
In the United States the federal agency responsible for safety-related issues of nuclear energy is the NRC (Nuclear Regulatory Commission).
Nuclear is any activity related to the nuclei of atoms as nuclear energy, nuclear fission, nuclear engineering, nuclear physics, etc.
The plural of nucleus is "nuclei" - watch the spelling. The energy is called "nuclear energy". It is potential energy related to the nuclear forces.
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Electrical energy is the energy generally stored in electrons and their movement. Nuclear energy is the energy stored with an atom. Electrons are a fundamental part of most atoms, thus nuclear energy also contains direct electrical energy.
Nuclear energy provides about 20 percent of US electricity, so it is useful. Atomic energy is the same thing, but is now an obsolete term, we use nuclear energy as the description now.
Nuclear energy is not related to the small particles that make up an object. It is derived from the nucleus of an atom through processes like nuclear fission or fusion.
Nuclear energy is a type of potential energy that is stored in the nucleus of an atom. When the nucleus of an atom undergoes a process called nuclear fission or fusion, this potential energy is released in the form of heat and kinetic energy, which can then be converted into electricity.
Chemotherapy and nuclear energy are not directly related. Chemotherapy is a form of cancer treatment that uses drugs to destroy cancer cells, while nuclear energy is a form of power generation that uses controlled nuclear reactions to produce electricity. However, some cancer treatments may use radioactive materials that are produced in nuclear reactors.