The speed of light is 3.0 x 10^8 m.s^-1. what is the speed in nm.ms^-1 ?
The Correct Answer and Explanation is :
To convert the speed of light from meters per second (m/s) to nanometers per millisecond (nm/ms), we need to break it down into two steps:
Step 1: Convert meters to nanometers
1 nanometer (nm) is equal to ( 1 \times 10^{-9} ) meters. So to convert the speed from meters to nanometers, we multiply by ( 10^9 ):
[
3.0 \times 10^8 \, \text{m/s} \times 10^9 \, \frac{\text{nm}}{\text{m}} = 3.0 \times 10^{17} \, \text{nm/s}
]
Step 2: Convert seconds to milliseconds
1 millisecond (ms) is equal to ( 1 \times 10^{-3} ) seconds. To convert the speed from seconds to milliseconds, we divide by ( 10^3 ) (because 1 ms is 1/1000th of a second):
[
\frac{3.0 \times 10^{17} \, \text{nm/s}}{10^3 \, \frac{\text{s}}{\text{ms}}} = 3.0 \times 10^{14} \, \text{nm/ms}
]
Final Answer:
Thus, the speed of light in nanometers per millisecond (nm/ms) is:
[
3.0 \times 10^{14} \, \text{nm/ms}
]
Explanation:
To convert from one unit to another, it’s important to know the relationships between the units involved. Here, we used the fact that:
- 1 meter = ( 10^9 ) nanometers
- 1 second = ( 10^3 ) milliseconds
By using these conversion factors, we were able to adjust both the unit of distance (meters to nanometers) and the unit of time (seconds to milliseconds), resulting in the final answer of ( 3.0 \times 10^{14} \, \text{nm/ms} ).
This conversion is necessary in many fields of physics, especially when dealing with phenomena on very small scales, like light in nanometer-sized wavelengths, and when timing is crucial on shorter scales, like milliseconds.