Exercises: Emission Spectra of Atoms

Describe what an emission spectrum of a gas looks like and how it differs from the continuous spectrum of a glowing light bulb filament. Why do different elements produce different line patterns?

A photon of green light has a frequency of $5.7 \times 10^{14}$ Hz. Find its energy in joules.

Rank these types of electromagnetic radiation from lowest to highest photon energy: visible light, X-rays, radio waves, infrared, ultraviolet. Explain the rule you used.

A hydrogen atom drops from an energy level of $-1.51$ eV to one of $-3.40$ eV. (a) Find the energy of the emitted photon in eV. (b) Convert it to joules, using $1\ \text{eV} = 1.60 \times 10^{-19}$ J. (c) Find the photon's wavelength.

A sodium streetlight emits strong yellow light at a wavelength of $589$ nm. (a) Find the frequency of this light. (b) Find the energy of one photon in joules. (c) The lamp emits $2.0 \times 10^{19}$ of these photons each second. Find the power carried by this light.

An atom has energy levels $E_1 = 0$, $E_2 = 2.0$ eV and $E_3 = 3.0$ eV. List every photon energy this atom can emit when it relaxes from level 3 to lower levels, including two-step paths. How many distinct spectral lines appear? Which line has the longest wavelength?

A student's spectrometer shows a gas emitting lines at $410$ nm, $434$ nm, $486$ nm and $656$ nm.

(a) Find the photon energy of each line in eV, using $hc = 1240\ \text{eV·nm}$. (b) Explain why a continuous-spectrum model of light could not account for these separate lines, but a photon model with energy levels can. (c) Suppose all four lines end on the same lower level. Argue whether the $656$ nm line comes from the highest or the lowest of the upper levels involved.

Astronomers at an observatory in Arizona photograph the light from a distant nebula and see bright lines at the same wavelengths as laboratory hydrogen, including $656$ nm. They also see a bright line at $501$ nm that they attribute to another element.

(a) Explain how the lines identify the elements in the nebula. (b) Find the photon energy of the $501$ nm line in eV, using $hc = 1240\ \text{eV·nm}$. (c) Explain why the nebula shows bright lines on a dark background, while a cooler gas cloud in front of a hot star produces dark lines on a bright background. (d) Describe what must be true of the energy levels for the dark and bright lines of the same element to occur at the same wavelengths.