Q. A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of α units, if light takes 6 min 40 s to cover this distance?

Q. A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of α units, if light takes 6 min 40 s to cover this distance?

 Given:

• New unit α = speed of light in vacuum = 3 × 10⁸ m/s
• Time for light to travel from Venus to Earth = 6 min 40 s

Step 1: Convert time to seconds

$$t = 6 \text{ min } 40 \text{ s} = (6 \times 60) + 40 = 360 + 40 = 400 \text{ s}$$

Step 2: Calculate the actual distance

$$\text{Distance} = \text{Speed of light} \times \text{Time}$$ $$d = (3 \times 10^8 \text{ m/s}) \times 400 \text{ s}$$ $$d = 1.2 \times 10^{11} \text{ m}$$

Step 3: Convert distance into α units

Since 1 α unit = 3 × 10⁸ m, we divide:

$$d_\alpha = \frac{1.2 \times 10^{11}}{3 \times 10^8}$$ $$\boxed{d_\alpha = 400 \ \alpha \text{ units}}$$