To solve this numerical, we determine the number of electrons, neutrons, and protons per molecule first. For methane ($CH_4$), carbon has 6 electrons and each hydrogen has 1, giving 10 electrons per molecule. Multiplying by Avogadro's number gives the total electrons in one mole. For $^{14}C$, the number of neutrons is $14 - 6 = 8$. We calculate the moles of $^{14}C$ in 7 mg, find the number of atoms, and then the total neutrons and their mass. Similarly, for $NH_3$, nitrogen has 7 protons and each hydrogen has 1, giving 10 protons per molecule. We find the moles of $NH_3$ in 34 mg to get the total number of molecules, protons, and their mass. Since the mass of the sample is fixed, changing temperature and pressure will not alter the number of protons.