Given:
Frequency of wave propagation, f = 5 x 10^8 rad/s
Phase constant, β = 3 x 10^8 units

To calculate the velocity of wave propagation in a conductor, we can use the formula:

v = ω/β

where v is the velocity of wave propagation, ω is the angular frequency, and β is the phase constant.

Substituting the given values into the formula:

v = (5 x 10^8 rad/s) / (3 x 10^8 units)

Simplifying the expression:

v = (5/3) units/s

Therefore, the velocity of wave propagation in the conductor is 5/3 units/s.

Explanation:
The velocity of wave propagation in a conductor is determined by the phase constant and the angular frequency. The phase constant represents the phase difference between two points in a wave. It is given in units such as meters or degrees.

The angular frequency, on the other hand, represents the rate at which the wave oscillates in radians per second. It is calculated by multiplying the frequency of the wave by 2π.

To find the velocity of wave propagation, we divide the angular frequency by the phase constant. This gives us the rate at which the wave travels through the conductor.

In this case, the given frequency is 5 x 10^8 rad/s and the phase constant is 3 x 10^8 units. Substituting these values into the formula, we can calculate the velocity of wave propagation.

The final answer is 5/3 units/s, which is option C.