First 11 objectives

what are the two properties of light as a wave?

Wavelength (λ) = distance between peaks in meters. Frequency (ν) = waves per second in Hz (s⁻¹).

Equation linking wavelength and frequency

c = λν

Speed of light (c)

3.00 × 10⁸ m/s

Relationship between λ and ν

Inverse: longer wavelength = lower frequency, shorter wavelength = higher frequency.

1 nm in meters

1 × 10⁻⁹ m. Always convert nm to m before calculating.

How to find ν from λ

ν = c / λ (the thing you are GIVEN goes on the bottom)

How to find λ from ν

λ = c / ν (the thing you are GIVEN goes on the bottom)

Electromagnetic spectrum from long λ to short λ

Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray

Visible light: longest and shortest λ

Red = longest λ (lowest ν). Violet = shortest λ (highest ν).

Photon

A single, smallest-possible packet (quantum) of light energy.

Quantized

Energy that comes only in fixed, indivisible amounts (stair steps, not a ramp).

Wave-particle duality

Light is BOTH a wave and a stream of particles. Which one you see depends on the experiment.

Experiment that shows light as a WAVE

Diffraction and interference

Experiment that shows light as a PARTICLE

The photoelectric effect

Photon energy and frequency

Higher frequency (shorter λ) = more energy per photon. X-rays have more energy than microwaves.

Photon energy equation (given frequency)

E = hν

Photon energy equation (given wavelength)

E = hc/λ (convert nm to m first)

Planck's constant (h)

6.626 × 10⁻³⁴ J·s

Which energy formula do I use?

Given frequency (Hz): E = hν. Given wavelength (nm or m): E = hc/λ.

Typical energy of one visible-light photon

About 10⁻¹⁹ J. If your answer is far from this, check your exponent.

Energy of a 500 nm photon

3.98 × 10⁻¹⁹ J

Moving the decimal in scientific notation

Front number must be between 1 and 10. Front number bigger = exponent smaller. Front number smaller = exponent bigger.

Dividing powers of ten

Subtract the bottom exponent from the top. Subtracting a negative means adding.

Ground state

The lowest energy level (n = 1).

Excited state

Any energy level above the ground state (n = 2, 3, ...).

Absorption

Atom takes in a photon, electron moves UP, atom gains energy, ΔE is positive.

Emission

Atom releases a photon, electron moves DOWN, atom loses energy, ΔE is negative.

Can an electron absorb a photon with slightly too little or too much energy?

No. The photon energy must EXACTLY match the gap between two levels.

Photoelectric effect

Light on a metal ejects electrons, but only if the light's frequency is above a threshold.

Threshold frequency

Minimum frequency of light that can eject electrons. Below it, no electrons come out no matter how bright the light is.

Work function (Φ)

Minimum energy needed to free an electron from a metal.

Kinetic energy of an ejected electron

KE = hν − Φ

Brighter light in the photoelectric effect

More photons, so MORE electrons. Speed stays the same.

Higher-frequency light in the photoelectric effect

Each photon has more energy, so electrons are FASTER. Number stays the same.

Light below the threshold frequency

No electrons are ejected, regardless of brightness.

Photoelectric question: brightness or color?

Bright/dim changes the NUMBER of electrons, not speed. Color/frequency changes the SPEED, not number.

Why the photoelectric effect proves light is a particle

Wave theory predicted bright light would work at any color and speed electrons up. Experiments showed a threshold, and brightness only changed the number. This fits one photon (hν) giving its energy to one electron.

Excitation

Electron moves UP to a higher level (gains energy). Same idea as absorption.

Relaxation

Electron moves DOWN to a lower level (loses energy, often as a photon). Same idea as emission.

Can a ground-state electron relax?

No. It is already at the lowest level, so it can only be excited.

Neon sign: excitation and relaxation

Electricity causes excitation. The glow comes from electrons relaxing and releasing photons.

One-electron species

Atom or ion with only one electron: H (Z = 1), He⁺ (Z = 2), Li²⁺ (Z = 3).

Energy change formula for one-electron species

ΔE = −2.18 × 10⁻¹⁸ J × Z² × (1/n_f² − 1/n_i²)

n_i and n_f

n_i = level where the electron starts. n_f = level where it ends. n_f goes first in the brackets.

Z² values

H: 1. He⁺: 4. Li²⁺: 9. Use Z², not Z.

Sign of ΔE

Positive = absorption (electron goes up). Negative = emission (electron goes down).

ΔE for hydrogen n = 2 to n = 1

−1.64 × 10⁻¹⁸ J (emission)

Steps for ΔE

1. Find n_i and n_f. 2. Do the brackets and keep the sign. 3. Multiply by −2.18 × 10⁻¹⁸ and Z². 4. Check sign and exponent.

de Broglie wavelength equation

λ = h / (mv)

Units for de Broglie equation

λ in meters, m in kg, v in m/s. Convert grams to kg by dividing by 1000.

Mass of an electron

9.109 × 10⁻³¹ kg

Why baseballs do not show wave behavior

Large mass makes λ extremely tiny (about 10⁻³⁴ m). Only very small particles like electrons have noticeable wavelengths.

Bigger mass or speed means what for wavelength?

Smaller wavelength (m and v are on the bottom of the fraction).

Calculator tip for de Broglie

Put the bottom in brackets: 6.626 EE −34 ÷ (m × v)

Quantum number n

Principal quantum number. Shell, size and energy. Values: 1, 2, 3, ...

Quantum number l

Angular momentum quantum number. Subshell, shape. Values: 0 up to n − 1.

Quantum number mₗ

Magnetic quantum number. Orbital orientation. Values: −l to +l including 0.

Quantum number mₛ

Spin quantum number. Only +½ or −½.

l letters

l = 0 is s, l = 1 is p, l = 2 is d, l = 3 is f

Number of orbitals in s, p, d, f

s: 1, p: 3, d: 5, f: 7 (equals 2l + 1)

Possible l values when n = 3

0, 1, 2 (subshells 3s, 3p, 3d). Include every number from 0 to n − 1.

Possible mₗ values when l = 1

−1, 0, +1 (3 orbitals)

Possible mₗ values when l = 2

−2, −1, 0, +1, +2 (5 orbitals)

Checklist for a possible set of quantum numbers

n: whole number 1 or higher. l: 0 to n − 1. mₗ: −l to +l (use the l from the question). mₛ: only +½ or −½. One failure = impossible.

Biggest trap with l

l can never equal n. The largest l is n − 1.

Is (n=2, l=2, mₗ=1, mₛ=+½) possible?

No. l must be 0 or 1 when n = 2.

Is (n=3, l=0, mₗ=1, mₛ=+½) possible?

No. When l = 0, mₗ can only be 0.

Is (n=3, l=2, mₗ=−2, mₛ=+½) possible?

Yes. It describes a 3d orbital.

Orbital (definition)

Region around the nucleus where an electron is most likely to be found. Not a fixed path.

Shape of an s orbital

Sphere. Only 1 per shell. Bigger n = bigger sphere.

Shape of a p orbital

Dumbbell (two lobes) with a node at the nucleus.

Names of the three p orbitals

pₓ, p_y, p_z (point along the x, y, and z axes at right angles)

Node

A spot where the electron is never found (the nucleus for a p orbital).

Larger orbital: 1s or 3s?

3s, because it has the bigger n.