Atoms

RPI - ERTH 2330

The Basis of All Materials

• Neutron - neutral particle• Proton - positively charged particle• Electron - negatively charged particle

E.B. Watson

The Atom

Visible light – part of the EM spectrum

Longer

v = f, and v = 299,792,458 m / s (~3 E 8) in a vacuumis length of a cycle in m, f is Hz (cycles per second)

Higher f

Our story begins with light…

FREQUENCY (f) number of cycles per unit time [units = Hertz (Hz)]

1 Hz = 1 cycle/sT = 1/f; f = 1/T; T f = 1

Wave Terms

Dispersion

High f – more “bending” in prism

Refraction – producing constituent wavelengths

RefractionWaves are bent as the move through materials with different wave propagating properties

E.B. Watson

The spectrum of the hydrogen atom

E.B. Watson

Violet 1 7.3E14 HzViolet 2 6.9E14 HzGreen 6.2E14 HzRed 4.6E14 Hz

What are the wavelengths (v=c)?

= v / f

Ph

oto

-Ele

ctri

c E

ffec

tP

ho

to-E

lect

ric

Eff

ect

Incident light causes movement of charge. Electrons move from the surface of the negatively-charged metal plate

The intensity of the light determines how many electrons are produced, but not their kinetic energy. Wavelength changes kinetic energy

Small packets, or quanta, possessing specific amounts of energy.

An incident photon is either totally absorbed by "target" matter or not absorbed at all*

The energy of the photons in a monochromatic beam of light

E = h f

h is (Planck’s constant 6.626 E -34 Js)

*Quantization of photons is like counting children - you can’t have a partial child

PHOTONS

Ephoton = EH - EL = h f

Energy transitions in Hydrogen

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1

λ= R

1

22 −1

n2

⎡ ⎣ ⎢

⎤ ⎦ ⎥

Line n

Violet 6

Violet 5

Blue-green 4

Red 3

Balmer relationshipsBalmer relationships

Any hot gas at low pressure will produce a line spectrum, although the spectra of other gases are more complex than that of hydrogen.

Hydrogen spectra

Bohr model - a "solar-system" model. assumptions:

•an electron is in specific "allowed" orbits•the allowed orbits are described by

m v r = n h / 2

Angular momentum Planck’s const.

F = m v2 / r and F = k q1 q2 / r2

Bohr saw this as charged particles on circular path set the forces equal

Bohr specific radii for electrons

j

kl

E.B. Watson

It requires energy to remove electrons

Energy increases with orbital distance.

Lowest energy configuration – ground state

2n

EE Ln =

Quantum number

Energy level at quantum number

Energy level at ground state

2n

EE Ln =

You can use this to determine changes in the amount of energy

12GL

n

E

n

EE −=Δ

Describes the change in energy of an electron moved from 1st orbital (the ground state in H) to the n orbital

E.B. Watson

Electrons are attracted to the protons in the nucleus. Great, how big is the nucleus?

E.B. Watson

E.B. Watson

E.B. Watson

Elements differ from one another by the number of protons they contain (Z)

Hydrogen (H) – 1 proton

Helium (He) – 2 protons

Sodium (Na) – 11 protons

Francium (Fr) – 87 protons

A neutralneutral atom will have as many electrons as protons.

Many atoms for each element will have the same number of neutrons as protons

Elements of the same Z that differ in the number of neutrons are isotopesisotopes.

AtomsAtoms

ElectronElectron

NeutronsNeutrons

ProtonProton

MassMass

9.109 E -31 kg9.109 E -31 kg

1.673 E -27 kg1.673 E -27 kg

1.673 E -27 kg1.673 E -27 kg

ChargeCharge

(-1) 1.602 E -19 coul.(-1) 1.602 E -19 coul.

(0) None(0) None

(+1) 1.602 E -19 coul.(+1) 1.602 E -19 coul.

Z = number of protons

N = number of neutrons

A = atomic mass number (N + Z)

Element = unique Z

Isotope = unique Z, different N

What happens to A? 14C

IsotopeSame Z, different N

Carbon (C ) Z = 6

Carbon-12 12C 6 protons, 6 neutrons 98.89%Carbon-13 13C 6 protons, 7 neutrons 1.11%Carbon-14 14C 6 protons, 8 neutrons trace

Atomic mass units (u)

Every isotope is scaled to 12C (12.000 u)

The total mass (“atomic weight”) of any element is the sum of the weighted mass of its isotopes.

For example, Oxygen has three isotopes

mass (rel 12C) Abundance

16O 15.99491 99.759%

17O 16.99914 0.037%

18O 17.00016 0.204%

(15.994191 x 0.99759) + (16.99914 x 0.00037) + (17.00016 x 0.00204) = 15.9994 u

•The interactions of electromagnetic radiation and electrons reveal the energy structure of the atoms

•The interaction of charged nuclei reveal the size of atomic nuclei

•The number of protons(+) determines the element’s identity

•It also determines the number of electrons (-)

•The number of electrons controls the behavior of the atom

•The number of neutrons may vary - isotopes

•Atomic mass is normalized to 12C

•Atomic mass for an element is a function of isotope abundance and mass.