How Do You Calculate Wavelength of Infrared Radiation in Micrometers?

In summary, to calculate the wavelength of infrared radiation with a frequency of 3.10 × 10^14 Hz, divide the speed of light (3.00 x 10^8 m/s) by the frequency and express the answer in scientific notation. However, when converting to micrometers, do not multiply by 1e-6 and be mindful of units.
  • #1
camboguy
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0

Homework Statement


Calculate the wavelength in micrometer of infrared radiation whose frequency is 3.10 × 10^14 Hz. Express answer in scientific notation. speed of light = 3.00 x 10^8 m/s


Homework Equations


wave length = speed of light/frequency



The Attempt at a Solution


1. so far i plugged in and i got 9.68 x 10^7 m/s Hz
2. then i converted the 9.68 x 10^7 to Micro meters
(9.68x10^7)( 1.0 x 10^-6) = (9.68 x 10^1 Micrometers/s Hz)?

is that the right answer?
 
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  • #2
Unfortunately - no.

3e8/3.1e14 is not 9.68e7

To convert meters to micrometers you don't multiply by 1e-6

Generally - watch your units, you will not miss the conversion then. What is Hz?
 
  • #3


Your attempt at solving the problem is on the right track. However, your final answer is incorrect. Here is the correct solution:

1. First, convert the frequency to Hz to mHz (10^-3 Hz) by dividing by 10^3: 3.10 x 10^11 mHz
2. Use the equation wavelength = speed of light/frequency to solve for the wavelength: wavelength = (3.00 x 10^8 m/s)/(3.10 x 10^11 mHz) = 9.68 x 10^-4 m
3. Finally, convert the wavelength to micrometers by multiplying by 10^6: wavelength = 9.68 x 10^-4 m x 10^6 = 968 micrometers
4. The final answer in scientific notation is 9.68 x 10^2 micrometers.
 

Related to How Do You Calculate Wavelength of Infrared Radiation in Micrometers?

1. What is a micrometer and how is it related to wave length?

A micrometer is a unit of measurement equal to one millionth of a meter. It is commonly used to measure small distances, such as the length of a wave. In the context of wave length, a micrometer is often used to measure the size of electromagnetic waves, such as light waves.

2. How is wave length measured in micrometers?

Wave length is typically measured in micrometers using a device called a spectroscope. This instrument uses diffraction grating or a prism to split light into its component wavelengths, allowing for precise measurement of the wave length in micrometers.

3. What is the significance of measuring wave length in micrometers?

Measuring wave length in micrometers is important because it allows scientists to understand the behavior and properties of electromagnetic waves, such as light, infrared, and ultraviolet waves. It also allows for the classification and categorization of different types of waves based on their wavelengths.

4. How does the wave length in micrometers affect the properties of electromagnetic waves?

The wave length in micrometers directly affects the properties of electromagnetic waves, such as their energy, frequency, and speed. Waves with shorter wavelengths have higher frequencies and carry more energy, while waves with longer wavelengths have lower frequencies and carry less energy.

5. Can wave length in micrometers vary for different types of electromagnetic waves?

Yes, the wave length in micrometers can vary for different types of electromagnetic waves. For example, visible light has a range of wavelengths between 380 to 750 micrometers, while radio waves can have wavelengths ranging from a few millimeters to several kilometers. This variation in wave length allows for the wide range of applications of electromagnetic waves in different fields of science and technology.

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