What exactly does the "per mole" unit of heat of atomization mean?

Question

I am facing a confusion in the definition of the standard enthalpy of atomization. The confusion arises because of the "per mole" in its units ($\pu{kJ mol^-1}$).

My question: When I say "per mole", do I mean "per mole" of the product or per mole of the reactant?

When I mean "per mole" of the product, my representative reaction for $\Delta H_\mathrm{a}^\circ$ is:

$$\ce{1/4 P4(s) -> P (g)}$$

And when I mean "per mole" of the reactant, my representative reaction for $\Delta H_\mathrm{a}^\circ$ is:

$$\ce{P4 (s) -> 4P (g)}$$

Using either of them leads to different calculations involving Hess's law or other chemical reactions, hence I feel there is a need to resolve this confusion.

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To add to this confusion, NCERT Chemistry (Part 1 page 171) writes:

It is the enthalpy change on breaking one mole of bonds completely to obtain atoms in the gas phase.

but then gives a representative reaction as:

$$\ce{CH4 -> C(g) + 4H(g)}$$

which involves breaking 4 moles of bonds instead.

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If someone could write the correct definition of the standard enthalpy of atomization, with more than one reputed reference to back their claim, it'd definitely resolve this confusion.

Answer 1

According to Wikipedia,

Standard enthalpy of atomization is the enthalpy change when $1$ mole of gaseous atoms is formed from its element in its defined physical state under standard conditions $(\pu{298.15K}, \pu{1 bar})$.

$\Delta H_{\text{at}}^{\circ}$ focuses on the production of $1$ mole of atoms from the element. Hence it's defined for the reaction:

$\ce{\dfrac{1}{8}S8 ->S}$

but not for the reaction:

$\ce{S8 -> 8S}$

So whenever you see the term "per mole", it is, by definition, implicitly referring to the product and not to the reactant.