A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance?

Sure, let's break this down:

1. We know that the speed of light is constant and it travels at a speed of approximately 300,000 kilometers per second (km/s) in a vacuum.

2. We're told that light takes 8 minutes and 20 seconds to travel from the Sun to the Earth. We need to convert this time into seconds because the speed of light is given in km/s. There are 60 seconds in a minute, so 8 minutes is 8*60 = 480 seconds. Adding the 20 seconds, we get a total of 500 seconds.

3. Now, we can calculate the distance light travels in this time. Since speed is distance divided by time, we can find the distance by multiplying the speed of light by the time it takes to travel. So, the distance from the Sun to the Earth is 300,000 km/s * 500 s = 150,000,000 kilometers.

4. But we're asked to find this distance in a new unit of length where the speed of light is unity, which means the speed of light is defined as 1 unit per second.

5. Since the speed of light is 1 unit per second in the new units, and it takes 500 seconds for light to travel from the Sun to the Earth, the distance between the Sun and the Earth is 500 units in the new system.

So, in terms of the new unit, the distance between the Sun and the Earth is 500 units.