Chinenye G. answered • 02/25/22
Chemistry, Biology and Statistics tutor
1 second = 9, 192,631,770 especially as it pertains to the properties of Cesium atom. So now to calculate wavelength you can use this and get your frequency, and you can use velocity, the speed of light.
You can use this equation:
Lambda = v/f
Where lambda or wavelength is what you are solving for, v is the velocity or speed of light constant 3.0x 10^8,. And f or frequency you just deciphered that this is Hz or seconds for Cesium. You can make this seconds inverse, s^-1,. And you will have that value expressed and then you can plug it into the equation.
1/s= 1/9,192,631,770= 1.088x10^-10. = HZ another way of expressing frequency unit.
Lambda = (3.0x10^8)/(1.088x10^-10)
Following your units will help you know how to resolve. The unit for wavelength is meters so the only way to resolve these two knowns and get meters in the end is to get it like this:
Essentially what you will be doing is 3.0x10^8(m/s)/9,192,631770s. And get units to cancel so you will have meters left. The base unit for the wavelength.
(3.0x10^8)* 1.088x10^-10. So that now your units are doing:. m/s*s/1. So seconds cancel out and you will finally have meters expressed.
This is really just the same as 3.0x10^8*1.088x10^-10=. This actually gives 0.03264 m. And since you know these units are in meters you can find this on the spectrum for light. 0.03264 m is the same as 3.264 cm because what you have to do is move the decimal place 2 places to the right to get to cm. Now looking at the spectrum of light what 3.264cm. Falls around the infrared/radio waves spectrum because it is somewhere between 1cm and 1m. The other result of 2.757x10^18 while evaluating this equation would leave the units with meters very high off the spectrum of wavelength of light. It would be going even beyond FM and AM radio waves. It would between Infrared and radio waves as the way these values would fall on the spectrum.
