The speed of light is 3.0 x 10^8 m/s. What is the speed of light in nm/s?
The Correct Answer and Explanation is :
To convert the speed of light from meters per second (m/s) to nanometers per second (nm/s), we need to use the fact that 1 meter (m) equals ( 1 \times 10^9 ) nanometers (nm). Here’s how the conversion works:
Conversion process:
- Start with the speed of light in meters per second:
[
3.0 \times 10^8 \, \text{m/s}
] - Multiply by the conversion factor from meters to nanometers:
[
3.0 \times 10^8 \, \text{m/s} \times \frac{1 \times 10^9 \, \text{nm}}{1 \, \text{m}}
]
The meters (m) cancel out, leaving:
[
3.0 \times 10^8 \times 10^9 \, \text{nm/s} = 3.0 \times 10^{17} \, \text{nm/s}
]
So, the speed of light is ( 3.0 \times 10^{17} \, \text{nm/s} ).
Explanation:
The speed of light is a fundamental constant in physics, often denoted by the symbol ( c ). Its value in meters per second is ( 3.0 \times 10^8 \, \text{m/s} ). To convert this to nanometers per second, we need to recognize that a nanometer is a billionth of a meter. This means that there are ( 1 \times 10^9 ) nanometers in one meter.
By multiplying the speed of light in meters per second by the conversion factor ( 1 \times 10^9 \, \text{nm/m} ), we effectively change the unit from meters to nanometers. Since we are working with exponents, we add the powers of 10: ( 10^8 ) from the speed of light in meters and ( 10^9 ) from the meter-to-nanometer conversion, resulting in ( 10^{17} ).
This conversion illustrates how changes in units can significantly impact the numerical value of a physical quantity, even though the actual physical speed remains the same. Nanometers are a much smaller unit of length, so the numerical value of the speed of light is vastly larger when expressed in nanometers per second.