Biophysics || very Flawless.
Structure of Matter:
Wave properties of particles, quantum properties of waves; correct answers 2. Wave properties
of particles
~Elementary particles possess (as do their systems: atoms, molecules) both corpuscular and wave
properties (corpuscular-wave dualism)
wave property ← diffraction and interference experiments show that light is represented by
waves
corpuscular property ← photoelectric effect demonstrates that light is a flux of energy in the
form of photons.
~Wave theory of matter: Motion of a particle with mass m, momentum p, and energy E is related
to the wavelength of de Broglie's wave by
λ = h/p
And to the frequency by f = E/h
~The equation for wavelength suggests that wavelengths of elementary particles are very short
(shorter than visible light). This is why the resolving power of an electron microscope is better
than that of an optical microscope.
*The energy E of photon (J) is related to the frequency f of the wave and to its wavelength lamda
(λ) by
E=hf = hc/ λ
where h = 6.63 x 10-34 J.s = 4.13x10-15 eV = Planks constant c=velocity of light
~The corpuscular-wave dualism has its consequences:
The Heisenberg Uncertainty Principle: it is impossible to determine with perfect accuracy the
position and momentum of a particle simultaneously. If the position vector r is being measured,
its momentum will change and vice versa.
3. Quantum properties of waves
Energy emitted from electromagnetic radiation comes in discrete bundles called quanta. The
energy value of a quantum is
E=hf = hc/ λ
This suggests a particulate nature of electromagnetic radiation where each light particle (photon)
carries an energy that is proportional to its frequency.
High frequency (short wavelength) → high energy
Low frequency (long wavelenth) → low energy
~The corpuscular-wave dualism has its consequences:
,The Heisenberg Uncertainty Principle: it is impossible to determine with perfect accuracy the
position and mome
Structure of Matter:
Quantum numbers correct answers Quantum numbers
The state (position and energy) of an electron can be described by a wave function composed of
dimensionless parameters which equal the degrees of freedom.
~The degrees of freedom of an electron = 4
~Thus, atomic theory states that the any electron in an atom can be completely described by 4
quantum numbers.
With the exception of the last quantum number ms (spin), the numbers determine the geometry
and symmetry of the electron cloud.
~The electron cloud is a space around the nucleus in which the probability of finding an electron
is high.
Pauli Exclusion Principle: no two electrons in a given atom can possess the same set of four
quantum numbers. (i.e. each electron in a given atom has a unique set of quantum numbers and
exist in the same quantum state)
1. Principle Quantum Number (n)
n = any positive integer 1, 2, 3, ...
n describes the electron's total energy and shell in which it can be found
~n = 1, 2, 3, 4, 5, 6, 7 corresponds to shell K, L, M, N, O, P, Q
The greater the value of n, the higher the energy level and radius of the electron's orbit
Maximum # of e- in energy level (shell) n = 2n2
*The difference in energy between two adjacent shells decreases with distance from the nucleus
(1/n12 - 1/n22)
n= total energy electron
M= 9.11x10 -31
E0= 8.854x10 -12 FM-1
e= 1.6x10 -19 coloumbs
2. Orbital Quantum Number (L)
For any given n, L is a number from 0 → n-1
It is determined by the angular momentum L where the magnitude of L =
Describes the subshell of the electron
Subshells s, p, d, f correspond to l values of 0, 1, 2, 3
Determines the shape of the orbital (s is spherical, p is bilobed, etc)
The max # of e- that can exist within a subshell = 4l + 2
3. Magnetic Quantum Number (ml)
Possible values are -l to +l
~For any value of l, there will be 2l +1 possibilities of ml
ex: l=0, s subshell
,Emission, ionization and excitation correct answers 6. Emission Spectrum of the hydrogen atom
~Electrons within an atom can be excited to higher energy levels when heat or other forms of
energy are applied. The excited state is not stable and short-lived. Thus the electron returns
rapidly to its initial state simultaneously emitting energy in the form of a photon.
~The energy of the released photon equals the energy difference between the excited and initial
states of the electron
~Since there are discrete values of electron energies only certain energies (frequencies,
wavelengths) may be emitted by the atom.
~The different electrons within the atom will be excited to different energy levels and each will
emit a photon characteristic of the energy transition it undergoes.
~Thus a line spectrum is produced with each line corresponding to a specific electron transition.
~Each element produces a unique emission spectrum that can serve as its fingerprint.
~The set of spectral lines observed during transitions from all higher levels into a certain energy
level corresponding to the given n is called a series.
The atomic emission spectra of hydrogen is composed of several series
Lyman Series: lines corresponding to e- transition from higher energy levels into the ground state
(n = 1)
I-observed in the ultraviolet region of light (high energy emission)
Balmer series: lines corresponding to e- transitions from higher energy levels into
n=2
-observed in the region of visible light
Paschen series: lines corresponding to e- transitions from higher energy levels into
n = 3 (Paschen's series) and to higher values of n
-observed in the region of infrared light (low energy emission)
*The greatest energy emitted is in the Lyman series and corresponds to an electron falling from n
= to n = 1
7. Ionization and Excitation
Electrons with minimum E are in the ground state
Exc
Structure of Matter:
Structure of electron shells in atoms correct answers 8. Structure of electron shells in atoms
Electron configuration is the pattern by which electrons fill an atom.
Electron filling is governed by two principles:
1. The arrangement is at minimal energy
2. No two electrons within the atom occupy the same quantum state
-electrons fill shells and subshells in order of increasing energy and each subshell is filled
completely before the next subshell begins filling
, -in the case of heavy atoms, higher shells can fill prior to lower ones if the total energy
associated with the shell is lower in the higher shell.
-highest # of electrons in a shell is 2n2
Closed shell/subshell: one that is completely occupied by electrons
s (2 e-), p (6 e-), d (10e-), f (14 e-)
-Total orbital and spin angular moment =0 and distribution of the electrons' eff charge is
symmetrical.
Hund's Rule: within a given subshell, orbitals are filled so that there are a maximum number of
half-filled orbitals with parallel spins.
-electrons prefer empty orbitals due to the repulsion of neg. charges that occurs in filled orbitals
-filled orbitals contain 2 e- with opposite spin
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6, 5s2, 4d10, 5p6, 6s2, 4f14, 5d10, 6p6, 7s2, 6d10
Structure of Matter:
Atomic nucleus correct answers 9. Atomic nucleus
The atomic nucleus is formed by nucleons: protons and neutrons
~It can be described by:
Atomic # = Z,
Mass # = A,
Neutron # = N = A - Z
~The total electrical charge Z of a nucleus is 1.6 x 10-19 C
~Most of the atom's mass is found in the nucleus (nucleon mass is 2 x 103 times greater than
electron mass)
~The mass of atoms is expressed in atomic mass units (AMU)
1 AMU = 1/12 the mass of a C-12 atom. 1 A.M.U.=1.66x10-27 kg = energy equivalent 931MeV
Isotopes- nuclei of the same element with same proton #, different neutron #
(same Z, diff A)
Isobars- nuclei with equal # nucleons, # different protons (same A, diff Z)
Isomers- same # of protons and neutrons but different energies of nuclei
-not stable, e- fall to lower energy levels → emit radiation
Radius of proton = 1.23x10-15 m
Radius of heavy atoms can be calculated Ra= (1.23x10-15) x A1/3
*atomic radii decrease from left to right on the periodic table and increase down a group
Nuclear forces hold an atom together via the strong interaction
~Range is 10-15 m
~Strength is not dependent on nucleon charge
~The strong interaction is the strongest force at this distance
Energy e- =0.51 MeV
Energy p =938MeV
Energy n =939MeV
Radius r =1.23x10-15 m
