Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm (c) When burned, a sample of an unknown substance is found to emit light of frequency 6.58 * 1014 s-1. Which of these elements is probably in the sample?

Question

Accepted Answer

Everyone in this example we have a sample of an unknown element burned and emitting light with a frequency of 1,311. Terror hurts. We need to identify the elements in the sample. Using the below information. And as you can see, we're given elements with their different wavelengths in nanometers. So we want to see which of these wavelengths gives us the identity of our element. And we want to recall our formula where the speed of light is equal to wavelength multiplied by our frequency. We want to recall that frequency should be in units of hertz. So we're going to convert the given frequency being 1,311. Terror hurts two hertz. So we would recall that our prefix Tera tells us that for one Terror hurts. We have 10 to the 12th power hurts. And this gives us our frequency in hertz as 1.311 times 10 to the 15th power hertz, which we can also interpret as 1.311 times 10 to the 15th power inverse seconds. Because we would recall that inverse seconds are equivalent to hertz. And so now solving for wavelength we're going to find our wavelength by setting that equal to the speed of light divided by our frequency. So what we would have is we should recall that our speed of light is equal to a value of 3.0 times 10 to the eighth power meters per second. And in our denominator we're going to plug in our frequency which we just converted to inverse seconds as 1.311 times 10 to the 15th power inverse seconds. So this is going to give us a value for our wavelength equal to 2.2883 times 10 to the negative seventh power. And as far as our units were going to be able to cancel out seconds with inverse seconds. Leaving us with meters as our units for wavelength. So we would have units of meters. However, we should recall that wavelength should be in units of nanometers. So we're going to convert from 2.28 83 times 10 to the negative seventh power meters in two nanometers. So we should recall that our prefix nano tells us that we have 10 to the negative ninth power meters for one nanometer. And now we're able to cancel out our units of meters, leaving us with nanometers as our final unit for wavelength, which is what we want. And this is going to give us a value equal to 228.8 nanometers. And so this would be our wavelength. So overall we're going to look at the data given to us in our prompt and looking at the only wavelength that has a value of 228 .8, we would see that that corresponds to the element cadmium. So we can say that therefore the unknown element is cadmium C. D. So this is our final answer here. If you have any questions please leave them down below. Otherwise, I'll see everyone in the next practice video.

Verified Solution

Key Concepts

Emission Spectra

Wavelength and Frequency Relationship

Quantization of Energy Levels