AP Chemistry 3.11-3.12: Spectroscopy and the Photoelectric Effect

Wave

An oscillation or periodic movement that transfers energy from one location to another without requiring the matter itself to travel with the wave.

How can a wave transfer energy while the medium remains essentially in place?

The particles of the medium oscillate locally and transfer energy to neighboring particles. For example, rope, water, and air particles move around equilibrium positions while the disturbance propagates.

What are the three fundamental properties used to characterize waves?

Wavelength, frequency, and amplitude. Wavelength is represented by $\lambda$, frequency by $\nu$, and amplitude describes the maximum displacement from equilibrium.

Wavelength ($\lambda$)

The distance between corresponding points on consecutive cycles of a wave, such as two adjacent crests or troughs. Its SI unit is the meter.

Frequency ($\nu$)

The number of complete wave cycles passing a fixed point per unit time. Its unit is the hertz, where $1\ \mathrm{Hz}=1\ \mathrm{s^{-1}}$.

Amplitude

The maximum displacement of a wave from its equilibrium position; it is one-half the vertical distance from crest to trough. For light, amplitude is related to intensity or brightness.

Electromagnetic wave

A wave consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation. Electromagnetic waves can travel through a vacuum.

What is the speed of electromagnetic radiation in a vacuum?

$c=2.998\times10^8\ \mathrm{m\,s^{-1}}$. This constant is used in relationships such as $c=\lambda\nu$ and $E=hc/\lambda$.

What is the relationship among wave speed, wavelength, and frequency?

Wave speed is given by $v=\lambda\nu$. For electromagnetic radiation in a vacuum, $c=\lambda\nu$, where $c=2.998\times10^8\ \mathrm{m\,s^{-1}}$.

How are wavelength and frequency related for electromagnetic radiation traveling in a vacuum?

They are inversely proportional because $c=\lambda\nu$. If wavelength increases, frequency decreases, and vice versa.

What do megahertz and gigahertz represent?

$1\ \mathrm{MHz}=1\times10^6\ \mathrm{Hz}$ and $1\ \mathrm{GHz}=1\times10^9\ \mathrm{Hz}$. These units are commonly used for radio-frequency electromagnetic waves.

How does changing the amplitude of light affect its intensity?

Increasing amplitude increases the light's intensity, observed as greater brightness. Amplitude does not determine the energy of an individual photon; photon energy depends on frequency.

How should the electromagnetic spectrum be understood in terms of wavelength and frequency?

It includes all types of electromagnetic radiation over a broad range of wavelengths and frequencies. Moving toward shorter wavelength corresponds to higher frequency, while longer wavelength corresponds to lower frequency.

What is the order of the major regions of the electromagnetic spectrum from longest wavelength to shortest wavelength?

Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Frequency and photon energy increase in this direction.

Where is visible light located in the electromagnetic spectrum?

Visible light occupies only a small portion of the electromagnetic spectrum, between infrared radiation at longer wavelengths and ultraviolet radiation at shorter wavelengths.

Why must wavelength units often be converted before using $c=\lambda\nu$?

The speed of light is normally expressed in meters per second, so wavelength should be converted to meters to maintain consistent units. For example, $589\ \mathrm{nm}=589\times10^{-9}\ \mathrm{m}$.

A light wave has a wavelength of $589\ \mathrm{nm}$. What is its frequency?

Using $\nu=c/\lambda$, $\nu=(2.998\times10^8\ \mathrm{m\,s^{-1}})/(589\times10^{-9}\ \mathrm{m})=5.09\times10^{14}\ \mathrm{Hz}$.

A cellular signal has a frequency of $850\ \mathrm{MHz}$. What is its wavelength?

Convert the frequency to $8.50\times10^8\ \mathrm{Hz}$ and use $\lambda=c/\nu$. The wavelength is approximately $0.353\ \mathrm{m}$.

Constructive and destructive interference

Constructive interference occurs when waves combine in phase, producing greater amplitude. Destructive interference occurs when a crest overlaps a trough, reducing or canceling the amplitude.

What evidence demonstrates the wave nature of light?

Light passing through two closely spaced slits produces interference fringes. Bright regions result from constructive interference and dark regions from destructive interference, behavior not explained by classical particles alone.

Continuous spectrum

A spectrum containing an unbroken range of wavelengths or frequencies. Heated solids, liquids, and high-pressure gases commonly produce continuous emission spectra.

Photon

A discrete packet of electromagnetic energy. The energy of one photon is $E=h\nu=hc/\lambda$.

How does photon energy depend on frequency and wavelength?

Photon energy is directly proportional to frequency, $E=h\nu$, and inversely proportional to wavelength, $E=hc/\lambda$. Higher-frequency or shorter-wavelength radiation has more energetic photons.

What is Planck's quantization relationship?

Planck proposed that oscillator energies occur in discrete amounts given by $E=n h\nu$, where $n=1,2,3,\ldots$ and $h=6.626\times10^{-34}\ \mathrm{J\,s}$.

What is the energy of a photon with wavelength $640\ \mathrm{nm}$?

Using $E=hc/\lambda$, $E=[(6.626\times10^{-34}\ \mathrm{J\,s})(2.998\times10^8\ \mathrm{m\,s^{-1}})]/(640\times10^{-9}\ \mathrm{m})=3.10\times10^{-19}\ \mathrm{J}$.

Photoelectric effect

The ejection of electrons from a metal surface when incident light has a frequency at or above a threshold frequency. It demonstrates that light transfers energy in discrete photons.

What is the threshold frequency in the photoelectric effect?

It is the minimum frequency of light capable of ejecting electrons from a particular metal. At the threshold, photon energy is just sufficient to overcome the metal's electron-binding energy.

What determines whether light can eject electrons from a metal in the photoelectric effect?

The light's frequency must be at least the metal's threshold frequency, meaning each photon must have enough energy to overcome the electron's binding energy. Increasing brightness cannot compensate for photons whose individual energies are too low.

How does increasing light frequency affect photoelectrons?

Above the threshold frequency, increasing frequency increases the kinetic energy of the ejected electrons because each photon carries more energy. The relationship follows $KE_{\max}=h\nu-\phi$, where $\phi$ is the metal's binding energy.

How does increasing light intensity affect the photoelectric effect?

If the frequency is above threshold, increasing intensity increases the number of photons striking the surface per unit time and therefore increases the number of emitted electrons. It does not increase the maximum kinetic energy of each electron.

How are wavelength and frequency changes related to the photoelectric effect?

Because $\nu=c/\lambda$, decreasing wavelength increases frequency and photon energy, increasing the kinetic energy of emitted electrons above threshold. Increasing wavelength lowers photon energy and may prevent electron emission.

How can a threshold frequency be converted into the binding energy per mole of electrons?

First calculate energy per photon using $E=h\nu$, then multiply by Avogadro's number: $E_{\mathrm{mol}}=h\nu N_A$. Divide by $1000$ to convert joules per mole to kilojoules per mole.

What does wave-particle duality mean for electromagnetic radiation?

Light exhibits wave behavior, such as interference and diffraction, and particle behavior, such as quantized photon energy and the photoelectric effect. Neither classical wave theory nor classical particle theory alone explains all observations.

Line spectrum

A spectrum containing discrete, narrow wavelengths or frequencies separated by regions with no emission. Excited low-pressure gases, such as those in neon signs, produce line spectra.

How do continuous and line emission spectra differ?

A continuous spectrum contains all wavelengths across a range, whereas a line spectrum contains only particular wavelengths. The discrete lines reflect specific allowed energy changes in emitting atoms or molecules.

What produces an emission spectrum?

Excited atoms or molecules emit photons as they transition from higher-energy states to lower-energy states. Because the allowed energy changes are discrete, the emitted light appears at specific wavelengths or frequencies.

What is an absorption spectrum?

A spectrum with dark lines or bands at specific wavelengths where atoms or molecules have absorbed photons. The absorbed wavelengths correspond to transitions from lower-energy states to higher-energy states.

How are the line positions in an absorption spectrum related to those in an emission spectrum?

For the same substance, absorption and emission lines occur at the same characteristic wavelengths because both result from the same allowed differences between quantized energy levels.

Why are atomic spectra useful in spectroscopy?

Each element has a characteristic set of allowed energy transitions and therefore a distinctive pattern of spectral lines. Identifying those lines can reveal the presence of particular elements.