Question

Speed of light in vacuum is :

• A. \(3 \times 10^8 \text{ km/s}\)
• B. \(3 \times 10^5 \text{ km/s}\)
• C. \(3 \times 10^7 \text{ km/s}\)
• D. \(3 \times 10^6 \text{ km/s}\)

Hint:

1. Speed of light in vacuum (\(c\)) \(\approx 3 \times 10^8\) meters per second (m/s). 2. To convert m/s to km/s, divide by 1000 (since 1 km = 1000 m). \(c \approx \frac{3 \times 10^8 \text{ m/s}}{1000 \text{ m/km}} = \frac{3 \times 10^8}{10^3} \text{ km/s}\) \(c \approx 3 \times 10^{(8-3)} \text{ km/s}\) \(c \approx 3 \times 10^5 \text{ km/s}\) This is \(300,000\) km/s.

Answer 1

The Correct Option is B

Concept: The speed of light in a vacuum, denoted by \(c\), is a fundamental physical constant. Its value is approximately \(3 \times 10^8\) meters per second (m/s). This question asks for the value in kilometers per second (km/s). Step 1: Recall the speed of light in m/s The speed of light in vacuum, \(c \approx 3 \times 10^8 \text{ m/s}\). This means \(c = 300,000,000 \text{ m/s}\). Step 2: Convert meters to kilometers We know that \(1 \text{ kilometer (km)} = 1000 \text{ meters (m)}\). Therefore, \(1 \text{ m} = \frac{1}{1000} \text{ km} = 10^{-3} \text{ km}\). Step 3: Convert the speed of light to km/s Substitute the conversion into the speed: \[ c = 300,000,000 \text{ m/s} = 300,000,000 \times \left(\frac{1}{1000} \text{ km}\right) / \text{s} \] \[ c = \frac{300,000,000}{1000} \text{ km/s} \] \[ c = 300,000 \text{ km/s} \] Step 4: Express this value in scientific notation To write \(300,000\) in scientific notation: Move the decimal point 5 places to the left to get 3.0. So, \(300,000 = 3 \times 10^5\). Therefore, the speed of light in vacuum is \(3 \times 10^5 \text{ km/s}\). Step 5: Compare with the options
(1) \(3 \times 10^8 \text{ km/s}\): This would be \(3 \times 10^{11} \text{ m/s}\), which is incorrect.
(2) \(3 \times 10^5 \text{ km/s}\): This matches our calculated value.
(3) \(3 \times 10^7 \text{ km/s}\): This would be \(3 \times 10^{10} \text{ m/s}\), incorrect.
(4) \(3 \times 10^6 \text{ km/s}\): This would be \(3 \times 10^{9} \text{ m/s}\), incorrect. The correct value is \(3 \times 10^5 \text{ km/s}\).