What are #"isotopes"#, and what is #"isopathy"#?

Answer 1

Isotopes are elements with different numbers of neutron contained in the nucleus..........

And radioisotopes are isotopes with unstable nuclei, so that they undergo radioactive decay to give stable isotopes. And, I think, isotherapy is some whack form of homeopathy that has no basis in evidence.

The number of protons, massive, positively charged nuclear particles present in the nucleus gives #Z#, #"the atomic number"#. For #Z=1#, we have the element hydrogen, for #Z=2#, helium, for #Z=3#, lithium,.......for #Z=23#, vanadium.
Now the number of protons determines the identity of the element, however, the nucleus can also contain #"neutrons"#, massive nuclear particles with ZERO charge. An atom can have differing numbers of neutrons, and this gives rise to the existence of isotopes.
If we take the simplest element, hydrogen, then #Z=1# by definition. Most hydrogen nuclei contain ONLY a proton, and this gives the protium isotope, #""^1H#. A few hydrogen nuclei contain a proton AND a neutron, and this gives the deuterium isotope, #""^2H#. A smaller few hydrogen nuclei contain a proton AND TWO neutrons, and this gives the tritium isotope, #""^3H#.
As #Z# gets larger, the heavier elements can support greater number of isotopes, and the atomic mass reported on the Periodic Table is the weighted average of the mass of the individual isotopes. Some isotopes are inherently unstable so that they undergo radioactive decay with the release of protons or neutrons to give new elements or new isotopes. #""^235U# is a famous fissile isotope that is used in the production of nuclear energy. These unstable isotopes are called #"radioisotopes"#. #"Radioisotopes"# are often used in medicine as a label, or as a means to target a particular cell.
#"Isotherapy"#, I have never heard of in a chemical context. I have heard homeopaths use the term, when they take minute substances (and I mean really dilute!) and use it to treat some illness. As far as I know this form of therapy has no evidentiary basis.
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Answer 2

Isopathy is a type of alternative medicine based on the idea that a substance that causes disease symptoms in healthy people can cure similar symptoms in sick people when given in highly diluted doses. Isotopes, on the other hand, are variations of a chemical element that have the same number of protons but different numbers of neutrons in their nuclei, resulting in different atomic masses.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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