Question

The speed of light is :

• A. \(3 \times 10^8 \text{ meter/sec}\)
• B. \(3 \times 10^{10} \text{ meter/sec}\)
• C. \(0.3 \times 10^8 \text{ meter/sec}\)
• D. \(0.03 \times 10^8 \text{ meter/sec}\)

Hint:

The speed of light in a vacuum (\(c\)) is a very important constant in physics. Remember it as approximately: \(c \approx 3 \times 10^8 \text{ m/s}\) This means light travels 300 million meters in one second! It's also common to see it as \(300,000 \text{ km/s}\) (since \(1 \text{ km} = 1000 \text{ m}\)).

Answer 1

The Correct Option is A

Concept: The speed of light in a vacuum (often denoted by \(c\)) is a fundamental physical constant. Step 1: Recalling the value of the speed of light The speed of light in a vacuum is a precisely defined value, but it is commonly approximated for most calculations. The accepted approximate value is \(300,000,000\) meters per second. Step 2: Expressing this value in scientific notation Scientific notation is a way of writing very large or very small numbers conveniently. To write \(300,000,000\) in scientific notation: Move the decimal point to the left until there is one non-zero digit before it. Here, we move it 8 places to the left: \(3.00000000\) Since we moved it 8 places to the left, we multiply by \(10^8\). So, \(300,000,000 \text{ m/s} = 3 \times 10^8 \text{ m/s}\). Step 3: Comparing with the options
(1) \(3 \times 10^8 \text{ meter/sec}\): This matches our calculated value.
(2) \(3 \times 10^{10} \text{ meter/sec}\): This is \(30,000,000,000 \text{ m/s}\), which is 100 times too large.
(3) \(0.3 \times 10^8 \text{ meter/sec}\): This is \(3 \times 10^7 \text{ m/s}\) or \(30,000,000 \text{ m/s}\), which is 10 times too small.
(4) \(0.03 \times 10^8 \text{ meter/sec}\): This is \(3 \times 10^6 \text{ m/s}\) or \(3,000,000 \text{ m/s}\), which is 100 times too small. The correct value is \(3 \times 10^8 \text{ meter/sec}\). (Sometimes written as \(2.99792458 \times 10^8 \text{ m/s}\) for high precision).