Final answer:
The angular resolution of the radio telescope at a frequency of 1.7 GHz is 5.60 minutes of arc.
Step-by-step explanation:
The angular resolution, which is the smallest angle by which two sources can be separated and still be recognized as two distinct sources, can be calculated using the Rayleigh criterion.
The Rayleigh criterion is given by the equation θ = 1.22λ/D, where θ is the angular resolution, λ is the wavelength of the radio waves, and D is the diameter of the radio telescope.
In this case, the radio waves have a wavelength of 4.00 cm and the telescope has a diameter of 300 m. Converting the wavelength to meters gives λ = 0.04 m.
Plugging in these values into the Rayleigh criterion equation, we can calculate the angular resolution:
θ = 1.22 * 0.04 m / 300 m = 0.00163 radians
To convert the angular resolution to minutes of arc, we use the fact that 1 radian is equal to 57.3 degrees or 3438 minutes of arc:
0.00163 radians * 3438 minutes of arc/radian = 5.60 minutes of arc
Therefore, the angular resolution of the radio telescope at a frequency of 1.7 GHz is 5.60 minutes of arc.