MCAT Physics and Math - Atomic and Nuclear Phenomena

535

photoelectric effect

When light of a sufficiently high frequency (typically, blue to ultraviolet light) is incident on a metal in a vacuum, the metal atoms emit electrons; light beams of greater intensity produce proportionally larger current; “all-or-nothing” response

current

net charge flow per unit time

threshold frequency (f_T)

minimum frequency of light that causes ejection of electrons; depends on the type of metal

if the frequency of the incident photon is less (f < f_T) → no electron will be ejected (insufficient energy)

if the frequency of the incident photon is more (f < f_T) → electron will be ejected (sufficient energy)

maximum kinetic energy of the ejected electron

equal to the difference between hf and hf_T; exact kinetic energy because the actual energy can be anywhere between 0 and K_max

K_max = hf − W = h(f - f_T)

photons

light beam consists of an integral number of light quanta

energy of photon

proportional to the frequency of the light

E = hf

where E is the energy of the photon of light, h is Planck’s constant, and f is the frequency of the light

Planck’s constant (h)

6.626 ×10⁻³⁴ J·s

work function

minimum energy required to eject an electron; related to the threshold frequency

W = hf_T

atomic absorption

electron can jump from a lower-energy to a higher-energy orbit by absorbing a photon of light of precisely the right frequency to match the energy difference between the orbits

atomic emission

an electron falls from a higher-energy level to a lower-energy level, a photon of light is emitted with an energy equal to the energy difference between the two orbits

infrared (IR) spectroscopy

determine chemical structure; different bonds will absorb different wavelengths of light

UV–Vis spectroscopy

the absorption of light by bonds in the visible and ultraviolet range

Absorption spectra

represented as a color bar with peak areas of absorption represented by black lines OR as a graph with the absolute absorption as a function of wavelength

phenolphthalein

indicator

acidic - transparent = absorb no visible light

basic - bright pink = absorbing all but the longer wavelengths of visible light

fluorescence

After being excited to a higher energy state by ultraviolet radiation, the electron in the fluorescent substance returns to its original state in two or more steps; at each step, a photon is emitted with a lower frequency (longer wavelength) than the absorbed ultraviolet photon

mass defect

difference between the sum of the masses of all of the protons and neutrons within it and the actual mass of every nucleus; result of matter that has been converted to energy

equivalence of matter and energy

E = mc²

where E is energy, m is mass, and c is the speed of light

1 g of mass = 89.9 TJ = 21.5 billion Kcal

nucleons

protons and neutrons, attracted by strong nuclear force

strong nuclear force

strong enough to more than compensate for the repulsive electromagnetic force between the protons; only acts over extremely short distances (less than a few times the diameter of a proton or neutron)

binding energy

bonded nucleons are at a lower energy level than the unbonded constituents; this difference in energy must be radiated away in the form of heat, light, or other electromagnetic radiation before the mass defect becomes apparent

weak nuclear force

contributes to the stability of the nucleus, but is about one-millionth as strong as the strong nuclear force

four fundamental forces of nature

1. strong nuclear force

2. weak nuclear force

3. electrostatic forces

   1. gravitation

isotopic notation

elements are preceded by their atomic number as a subscript and mass number as a superscript

^A_ZX

atomic number (Z)

the number of protons in the nucleus

mass number (A)

the number of protons plus neutrons

Fusion

a process by which small nuclei combine to form a larger nucleus

ex. stars (hydrogen → helium); power plants

Fission

a process by which a large nucleus splits into smaller nuclei; rarely spontaneous; often requires the absorption of a low-energy neutron

Radioactive decay

naturally occurring spontaneous decay of certain nuclei accompanied by the emission of specific particles

parent nucleus (X)

undergoes nuclear decay

daughter nucleus (Y)

formed from nuclear decay

Isotope Decay Arithmetic

^A_ZX → ^A’_Z’Y + emitted particle

the sum of the atomic numbers and the mass numbers must be the same on both sides

Alpha decay

emission of an α-particle

^A_ZX → ^A-4_Z-2Y + ⁴₂α

α-particle

two protons, two neutrons, and zero electrons; massive; twice the charge as β-particle; interact with matter; low penetrating power

⁴₂He

Beta decay

a neutron decays into a proton, β^--particle, and an antineutrino (ν)

^A_ZX → ^A_Z+1Y + β⁻

β-particle

an electron; very light; more penetrating than alpha radiation

e^- or β^-

positron emission

proton is converted into a neutron, a β⁺-particle, and a neutrino

^A_ZX → ^A_Z-1Y + β⁺

positron

mass of an electron but carries a positive charge

e⁺ or β⁺

Gamma decay

emission of γ-rays without changing the mass number or the atomic number; high-energy state of the parent nucleus may be represented by an asterisk

^A_ZX* → ^A_ZX + γ

γ-rays

high-energy (high-frequency) photons; no charge; lower the energy of the parent nucleus

Electron capture

rare process; reverse of β⁻ decay

^A_ZY + e⁻ → ^A_Z-1Y

half-life (T_1/2)

time it takes for half of the sample to decay; asymptotically approaches zero

exponential decay

the rate at which the nuclei decay is proportional to the number that remain

n = n0e^−λt

where n0 is the number of undecayed nuclei at time t = 0

decay constant & half-life