Q.At what temperature will oxygen molecules have the same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively)

[!TLDR] Equal rms speeds means T/M is the same for both gases; solve for the oxygen …

Setting the rms speeds of oxygen (at unknown temperature T) and helium (at S.T.P., 273 K) equal: sqrt(3RT_O2/M_O2) = sqrt(3RT_He/M_He), which simplifies to T_O2/M_O2 = T_He/M_He. Solving for T_O2: T_O2 = T_He × (M_O2/M_He) = 273 × (32/4) = 273 × 8 = 2184 K. So oxygen must be heated to 2184 K for its molecules to have the same rms speed as helium mole …

Equate v_rms formulas for both gases, cancel the common factor of 3R, and …

Using an incorrect value for S.T.P. temperature (it is 273 K = 0 ºC, not 298 K or another value), or inverting the …