The electron drift mobility in 𝛤 conduction band of GaAs has been calculated before, but for the first time, we have made attempts to estimate the electron mobilities in higher energy L and X minima. We have also calculated the value of mobility of two-dimensional electron gas needed to predict hetero-structure device characteristics using GaAs. Best scattering parameters have been derived by close comparison between experimental and theoretical mobilities. Room temperature electron mobilities in 𝛤, L and X valleys are found to be nearly 9094, 945 and 247 cm² /V-s respectively. For the above valleys, the electron masses, deformation potentials and polar phonon temperatures have been determined to be (0.067, 0.22, 0.39m 0 ), (8.5, 9.5, 6.5 eV), and (416, 382, 542 K) as best values, respectively. The 2-DEG electron mobility in 𝛤 minimum increases to $1.54 \times 10^{6}$ from $1.59 \times 10^{5}$ cm² /V-s (for impurity concentration of 10¹⁴ cm^-3) at 10 K. Similarly, the 2-DEG electron mobility values in L and X minima are estimated to be $2.28 \times 10^{5}$ and $1.44 \times 10^{5}$ cm² /V-s at 10 K, which are about $\sim 4.5$ and $\sim 3.9$ times higher than normal value with impurity scattering present.