 Solution

At nucleosynthesis temperatures, $50\mathrm{GeV}$ particles are nonrelativistic. Their equilibrium abundance is negligible because of Boltzmann suppression, so they do not behave as an extra relativistic species contributing its full degree count to $g_{\ast }$. A stable thermal weakly interacting massive particle generally freezes out much earlier; a surviving relic population with the usual dark-matter abundance remains negligible compared with radiation during nucleosynthesis. In that standard relic scenario the helium abundance is essentially unchanged.

The mass and weak coupling alone do not specify the relic density. If an unusually abundant stable population contributes appreciably to the expansion density, it raises $H$ at fixed radiation temperature and increases helium by the same freeze-out and survival mechanism as part (g). Decays or energetic annihilation products would require their own specified history. Thus a universal numerical change cannot be inferred from the mass alone.