Final answer:
The propagation constant γ for a transmission line is calculated with the formula γ = √((R + jωL)(G + jωC)); however, the exact numerical value cannot be determined without the angular frequency ω.
Step-by-step explanation:
To calculate the propagation constant γ for a transmission line, we use the primary per unit length parameters given: inductance L = 0.3 μH/m (microhenrys per meter), capacitance C = 500 pF/m (picofarads per meter), resistance R = 5 Ω/m (ohms per meter), and conductance G = 0.02 S/m (siemens per meter). The propagation constant γ is a complex number represented by γ = α + jβ, where α is the attenuation constant and β is the phase constant. To find γ, we use the formula γ = √((R + jωL)(G + jωC)), where j is the imaginary unit and ω is the angular frequency of the signal on the transmission line (which is not provided in the given parameters).
Without the angular frequency ω, we cannot calculate the exact numerical value for γ; however, the formula provided expresses the relationship between the propagation constant and the physical parameters of the transmission line.