1. Lecture 12: The Atom & X-Rays
Bohr Model
Quantum Model
Quantum Numbers
Pauli Exclusion Principle
Electron Configuration
X-Rays
Production
Types
Nuclear Physics

2. Bohr Atom
Using Newton’s Second Law, circular motion, Coulomb’s Law, and quantized angular momentum, we can predict…
Energy levels of electrons in an atom:
The radius of electrons is orbit in an atom:
(Z is the atomic number of the atom)

3. Atomic Spectra
When electrons change energy levels in the atom, energy is either absorbed by or emitted from the atom. This is done through the absorption or emission of a photon!
All the possible transitions of electrons in an atom (for example, hydrogen) make up the spectral lines for that element.

4. Atomic Spectra
n=4
Although not every photon in the spectrum of an atom are visible, each transition represents a photon given off by the atom.
Spectra can be used to determine what an unknown gas is or what elements make up an object (such as stars).
n=3
n=2
n=1

5. Quantum Atom Bohr was wrong… The quantum atom…
The energy levels and approximate size were correct.
However, quantized electron velocity and radius violates the Heisenberg uncertainty principle.
The quantum atom…
Predicts energy states agreeing with Bohr.
Does not have definite electron positions, only a probability function.
Each orbital can have 0 angular momentum.
Each electron has 4 quantum numbers (next lecture).

6. Summary of Concepts Bohr Model Quantum Model
Provides electron radius and energy.
Calculates spectral lines of atoms.
Quantum Model
Involves probabilities and uncertainty.
Electrons have quantum numbers.

7. Example
Calculate the wavelength of a photon emitted when an electron in an excited hydrogen atom drops down to a lower level. Use the electron transition form the third excited state to the first excited state.
(This transition corresponds to this line in hydrogen’s spectrum.)

8. Example
Calculate the energy of each state:
= eV
= -3.4 eV

9. Example
Now find the wavelength associated with this transition:
= 487 nm

10. Quantum Numbers
Each electron in an atom is labeled by four quantum numbers:
n = principle quantum number (1, 2, 3, …)
determines energy
ℓ = orbital quantum number (0, 1, 2, … , (n – 1))
determines angular momentum
m ℓ = magnetic quantum number (- ℓ, … , 0, … , + ℓ)
component of ℓ
ms = spin quantum number (+½ or –½)
“up spin” or “down spin”
Subshells:
ℓ = 0 is the “s subshell”
ℓ = 1 is the “p subshell”
ℓ = 2 is the “d subshell”
etc.

11. Pauli Exclusion Principle
In any atom, each electron must have a different set of quantum numbers (only one electron is allowed in each quantum state).
This explains the periodic table:
Only two electrons can have a quantum number n = 1 (since then ℓ = 0, mℓ = 0 and ms can be +½ or –½). Thus there are only two elements in the top row.
Only eight electrons can have a quantum number n = 2 (two electrons for ℓ = 0 just like above and then six for ℓ = 1 since mℓ can be -1, 0, or +1 and ms can be +½ or –½ for each of those). Thus there are only eight elements in the second row.
Etc.

12. Electron Configurations
Electron configurations for atoms:
H  1s1 (n = 1, ℓ = 0, 1 electron)
He  1s2 (n = 1, ℓ = 0, 2 electrons)
Li  1s22s1 (n = 1, ℓ = 0, 2 electrons) and (n = 2, ℓ = 0, 1 electron)
Be  1s22s2 (n = 1, ℓ = 0, 2 electrons) and (n = 2, ℓ = 0, 2 electrons)
B  1s22s22p1 (n = 1, ℓ = 0, 2 electrons) and (n = 2, ℓ = 0, 2 electrons) and (n = 2, ℓ = 1, 1 electron)
Ne  1s22s22p6 (n = 1, ℓ = 0, 2 electrons) and (n = 2, ℓ = 0, 2 electrons) and (n = 2, ℓ = 1, 6 electrons)

13. Summary of Concepts Quantum Numbers Pauli Exclusion Principle
Four numbers for each electron.
Pauli Exclusion Principle
Each electron must hae a differnet set of quantum numbers.
Electron Configuration
Represent the elements in the periodic table.

14. Example
What is a possible set of quantum numbers for the outermost electron (in its ground state) in a Sodium atom?

15. Example Since we know n = 3, we have three choices for ℓ: 0, 1, or 2.
Looking at the periodic table, sodium is the first element in row three, so we are dealing with the s subshell (ℓ = 0).

16. Example
The spin quantum number is arbitrary, so we will give it a spin of –½:

17. X-Ray Production
X-rays are photons in the approximate range of 100eV to 100,000 eV.
X-rays go right through you (due to high energy) except for your bones…
X-rays are not easy to produce:
(Transitions of outer electrons in atoms are around 10 eV.)
(Radioactive decay produces X-rays that are hard to regulate.)
X-rays can be produced through slamming high energy electrons (up to 100,000 eV) into heavy atoms.

18. Types of X-Rays Brehmsstrahlung Characteristic (Kα and Kβ)
Produced when electrons hit atoms and slow down, losing KE and emitting energy as an x-ray
X-rays produced will have a range of energy, but there is a maximum (if all electron energy is transferred to the x-ray)
Characteristic (Kα and Kβ)
Produced when an electron knocks out ground state electrons from an atom, and another electron replaces it, giving off energy as an x-ray
Kα x-rays are when the replacing electron comes from the first excited state
Kβ x-rays are when the replacing electron comes from the second excited state (not as likely, but possible)

19. Nuclear Physics A Z The nucleus is composed of protons & neutrons:
Z = number of protons in the nucleus
N = number of nuetrons in the nucleus
A = total number of protons and nuetrons
N ≈ Z for lower atomic numnbers
N > Z for higher atomic numbers A Z

20. Summary of Concepts X-Ray Production X-Ray Types Nuclear Physics
Procuded through change in energy of electrons bumping into other heavier atoms.
X-Ray Types
Brehmsstrahlung
Characteristic
Nuclear Physics
The nucleus is composed of protons and neutrons.

21. Example
If an X-ray is produced by an electron with 58,000 eV of energy, what is the minimum wavelength it can have?

22. Example
 = 2.1 x m