Module 2

Question 1

Quantization

Answer 1

When an electron is “confined” (attractive forces between the electron and the proton) to a finite region of space by the forces exerted on it, its total energy is restricted to certain special values.

Question 2

Light

Answer 2

Electromagnetic (EM) radiation that transmits energy through space or some other medium. Has an electric field that oscillates at a certain frequency and a magnetic field that oscillates at the same frequency perpendicular to the plane of the electric field.

Question 3

Electromagnetic Radiation

Answer 3

Produced when electrical charges (electrons) undergo some sort of acceleration.

Question 4

Wavelength (λ)

Answer 4

Distance between successive maxima in metres.

Question 5

Period (T)

Answer 5

Time it takes for the electric field to return to its maximum strength in seconds.

Question 6

Frequency (v)

Answer 6

The number of times per second the electric field reaches its maximum value in Hz OR 1/s. 1/T.

Question 7

The Speed of Light (c)

Answer 7

2.998 x 10^8 m/s

Question 8

Visible Light

Answer 8

Wavelength range 400 nm (violet) to 750 nm (red).

Question 9

The Electromagnetic Spectrum

Answer 9

High Energy

y rays
x-rays
ultraviolet
visible
infrared
microwave
radiowave

Low Energy

Question 10

Node

Answer 10

Areas of low electron density.

Question 11

Experiments That Support the Concept of Energy Being Quantized at the Molecular Level

Answer 11

1) Blackbody Radiation
2) The Photoelectric Effect
3) Line Spectra of Atoms

Question 12

Blackbody Radiation

Answer 12

Regardless of composition, an object at 300 K will emit light in the mid-IR (infrared) region.

Question 13

Blackbody Radiation Experiment (1850s)

Answer 13

A heated solid produces electromagnetic radiation that consists of many wavelengths. The emitted radiation is passed through a prism to split the light into its component wavelengths. We can generate an intensity profile by measuring the intensity (I) of light for each of the wavelengths emitted. Classical Theory did not match the results. In 1900, Max Planck proposed that the energy of oscillation is restricted to certain values (Eosc = nhv).

Question 14

Planck’s Constant (h)

Answer 14

6.626 x 10^-34 J s

Question 15

The Photoelectric Effect (1887)

Answer 15

Heinrich Rudolf Hertz. Light is used to dislodge electrons from the surface of a metal. The maximum kinetic energy of the ejected electrons was monitored as a function of the frequency (v) and intensity (I) of the incident light. Electrons were ejected only if the frequency of light was greater than some “threshold” frequency, Vo. For v >/ vo, the kinetic energy (KE) of an ejected electron increased proportionally with v. Provided v >/ vo, electrons were ejected instantaneously (no time delay) regardless of the intensity of the incoming light. When KEe- vs v is plotted, the slope of the line is equal to Planck’s constant. Overall, the energy of light is highly localized and is proportional to its frequency (Ephoton = hv).

Question 16

Einstein’s Explanation of the Photoelectric Effect (1905)

Answer 16

Proposed that the energy of light cannot be spread out over the entire wave. It must be concentrated into small, particle-like bundles (photons). The energy of a photon must be proportional to the frequency of the light. The energy of an incoming photon is transferred instantly to an e- at the surface. The energy of the photon is used to dislodge the e- from the surface and the excess energy is converted into kinetic energy of the ejected e-. The collision of a photon and an electron at the surface obeys conservation of energy (Ephoton = w + (KE)e-). Overall, the energy of light is highly localized and is proportional to its frequency (Ephoton = hv).

Question 17

Work Function (w)

Answer 17

The minimum energy required to dislodge an electron from the metal’s surface.

Question 18

Line Spectra of Atoms

Answer 18

White light can be dispersed into a rainbow of colours using a prism (a continuous spectrum). If you place a sample of atomic gas (ex. H) between the light source and the prism, dark lines appear, suggesting certain quanta of energy were absorbed by the atomic gas. Alternatively, if the light emitted from a sample of high energy atoms is dispersed into its component wavelengths, only certain colours of lines appear. The energy of a photon was determined by the colour of the light.

Question 19

Continuous Spectrum

Answer 19

Full rainbow.

Question 20

Absorption Spectrum

Answer 20

Rainbow with black lines.

Question 21

Emission Spectrum

Answer 21

Black background with a few rainbow lines.

Question 22

Neils Bohr

Answer 22

Postulated that the e- moved around the nucleus with speed v in a circular orbit of radius r. The stable orbits were those for which the stated condition holds. When the electron “drops” (transitions) from a higher energy level (Eupper) to a lower energy level (Elower), the atom emits a photon with energy equal to Eupper - Elower (ΔE is negative). In order for the electron to “jump” (transition) from a lower energy level to a higher energy level, the atom must absorb a photon with energy equal to Eupper - Elower (ΔE is positive).

Question 23

De Broglie’s Hypothesis

Answer 23

Particles exhibit a wave-particle duality.

Question 24

The Heisenberg Uncertainty Principle

Answer 24

We can never know the “true” behaviour of a system. It is impossible to know simultaneously both the position and the momentum of a particle with absolute certainty.

Question 25

Diffraction

Answer 25

Observed when light passes through a hole or slit where size is comparable to the wavelength of the light (λ of the light source matches the hole in the film).

Question 26

Δx

Answer 26

Uncertainty in the position of the particle relative to the nucleus.

Question 27

Δp (mΔv)

Answer 27

Uncertainty in the momentum of the particle.

Question 28

Position

Answer 28

Fixed location in space at a point in time.

Question 29

Momentum

Answer 29

Motion of mass.

Question 30

Principal Quantum Number (n)

Answer 30

Determines the “size” of an orbital (1 —> ∞)

Question 31

Orbital Angular Momentum Quantum Number (l)

Answer 31

Determines the “shape” of an orbital (0 —> n-1)

Question 32

Magnetic Quantum Number (ml)

Answer 32

The number of distinct orientations that are allowed for a particular orbital (-I —> +l).

Question 33

Ψ^2

Answer 33

The probability of finding the e- or the density of the electron cloud.

Question 34

Radial Factor

Answer 34

Dependent on the distance between e- and nucleus. Impacts the size of the orbital (n, l).

Question 35

Angular Factor

Answer 35

Where the e- is around the nucleus. Impacts the shape and orientation of the orbital (l, ml).

Question 36

Number of Radial Nodes

Answer 36

n - l - 1

Question 37

Number of Angular Nodes

Answer 37

l

Question 38

Total Number of Nodes

Answer 38

n - 1

Question 39

Rmp

Answer 39

Most probable radius.

Question 40

Bohr Radius

Answer 40

52.9 pm

Question 41

Schrodinger’s Equation

Answer 41

The state of an electron is characterized by three quantum numbers, n, l, and ml.

Question 42

s and ms

Answer 42

Quantum numbers associated with the spin of the electron.