The reactivity of hydrogen atoms attached to different carbon atoms in alkanes can be explained by considering the stability of the resulting alkyl radicals formed during a reaction. The stability of alkyl radicals is influenced by the number of alkyl groups attached to the carbon atom bearing the unpaired electron.

Tertiary > Secondary > Primary Reactivity:

1. Tertiary Hydrogen Atom Reactivity:
Tertiary carbon atoms are bonded to three alkyl groups. When a tertiary hydrogen atom is removed, a tertiary alkyl radical is formed. Tertiary alkyl radicals are highly stable due to the electron-donating inductive effect from the three alkyl groups. The stability of the alkyl radical decreases the reactivity of the hydrogen atom, making it less likely to participate in a reaction.

2. Secondary Hydrogen Atom Reactivity:
Secondary carbon atoms are bonded to two alkyl groups. When a secondary hydrogen atom is removed, a secondary alkyl radical is formed. Secondary alkyl radicals are relatively less stable than tertiary alkyl radicals. The presence of two alkyl groups provides some stability to the radical, but it is lower compared to tertiary alkyl radicals. Therefore, secondary hydrogen atoms have higher reactivity compared to tertiary hydrogen atoms.

3. Primary Hydrogen Atom Reactivity:
Primary carbon atoms are bonded to only one alkyl group. When a primary hydrogen atom is removed, a primary alkyl radical is formed. Primary alkyl radicals are the least stable among the three types. The absence of any alkyl groups to stabilize the radical makes primary hydrogen atoms highly reactive.

Conclusion:
Based on the stability of the resulting alkyl radicals, the reactivity of hydrogen atoms attached to different carbon atoms in alkanes follows the order: Tertiary > Secondary > Primary. This pattern can be explained by the electron-donating inductive effect from alkyl groups, which increases the stability of the resulting alkyl radicals.