How Do You Calculate Wavelength of Infrared Radiation in Micrometers?

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SUMMARY

The wavelength of infrared radiation with a frequency of 3.10 × 1014 Hz is calculated using the formula: wavelength = speed of light / frequency. The correct calculation yields a wavelength of approximately 9.68 × 10-7 meters, or 968 micrometers. A common mistake involves incorrect unit conversion, particularly when converting from meters to micrometers, which requires multiplying by 1.0 × 106 instead of 1.0 × 10-6.

PREREQUISITES
  • Understanding of the speed of light (3.00 × 108 m/s)
  • Familiarity with frequency units (Hertz)
  • Knowledge of unit conversion between meters and micrometers
  • Basic algebra for manipulating equations
NEXT STEPS
  • Learn about the electromagnetic spectrum and the properties of infrared radiation
  • Study unit conversion techniques, particularly in scientific notation
  • Explore the implications of frequency and wavelength in wave mechanics
  • Investigate the applications of infrared radiation in technology and science
USEFUL FOR

Students in physics, educators teaching wave mechanics, and anyone interested in the properties and calculations related to infrared radiation.

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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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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?
 

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