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?

Verified step by step guidance

1. Identify the relationship between wavelength (\(\lambda\)) and frequency (\(\nu\)) using the equation \(c = \lambda \nu\), where \(c\) is the speed of light (\(3.00 \times 10^8\) m/s).
2. Rearrange the equation to solve for wavelength: \(\lambda = \frac{c}{\nu}\).
3. Substitute the given frequency (\(6.58 \times 10^{14}\) s\(^{-1}\)) into the equation to calculate the wavelength in meters.
4. Convert the wavelength from meters to nanometers by multiplying by \(1 \times 10^9\) nm/m.
5. Compare the calculated wavelength with the characteristic wavelengths of the elements provided in the table to identify the element present in the sample.

Key Concepts

Emission Spectra

Emission spectra are unique patterns of light emitted by elements when they are energized, such as by heat or electricity. Each element emits light at specific wavelengths, which correspond to the energy transitions of electrons within the atoms. By analyzing these wavelengths, chemists can identify the presence of particular elements in a sample.

Wavelength and Frequency Relationship

The relationship between wavelength and frequency is described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This means that as the frequency of light increases, its wavelength decreases, and vice versa. Understanding this relationship is crucial for converting the given frequency of light emitted by the unknown substance into a wavelength to compare with known emission wavelengths.

Identifying Elements through Spectroscopy

Spectroscopy is a technique used to identify elements based on their emission or absorption of light at specific wavelengths. By comparing the emitted light from a sample to known wavelengths of various elements, chemists can determine which elements are present. In this case, the frequency of the emitted light can be converted to a wavelength to match against the characteristic wavelengths provided for different elements.