The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are:

First, we recall the definition of isotopes: isotopes are nuclides that have the same atomic number $$Z$$ (same number of protons) but different mass numbers $$A$$ (different total number of protons and neutrons). In nuclear notation an isotope is written as $$^{A}_{Z}\text{X}$$, where $$\text{X}$$ is the chemical symbol of the element.

Hydrogen has atomic number $$Z = 1$$, so all of its isotopes must contain exactly one proton. The known naturally occurring isotopes of hydrogen are:

1. $$^{1}_{1}\text{H}$$, called protium. 2. $$^{2}_{1}\text{H}$$, called deuterium and sometimes written as $$\text{D}$$. 3. $$^{3}_{1}\text{H}$$, called tritium and sometimes written as $$\text{T}$$.

Now we count the total number of distinct isotopes listed above. We have clearly enumerated three different mass numbers: $$A = 1, 2, 3$$. So the total number of hydrogen isotopes is

$$\text{Total isotopes} = 3.$$

Next, we determine which of these isotopes are radioactive. A radioactive isotope is one whose nucleus is unstable and undergoes spontaneous decay, emitting radiation. We know from experimental nuclear data that

• Protium $$\left(^{1}_{1}\text{H}\right)$$ is perfectly stable. • Deuterium $$\left(^{2}_{1}\text{H}\right)$$ is also stable. • Tritium $$\left(^{3}_{1}\text{H}\right)$$ is unstable (radioactive) with a half-life of about $$12.3$$ years, undergoing $$\beta^{-}$$ decay to form helium-3.

Therefore, the number of radioactive isotopes among hydrogen’s three isotopes is

$$\text{Radioactive isotopes} = 1.$$

So we arrive at the ordered pair $$\bigl($$ total number of isotopes $$,\;$$ number of radioactive isotopes $$\bigr) = (3,\,1).$$

Looking at the options given in the question, Option C states “3 and 1,” which exactly matches our derived pair.

Hence, the correct answer is Option C.