Chapter 9: Atomic and Nuclear Phenomena Flashcards
Threshold frequency, Ft
The minimum frequency of light that causes ejection of electrons is known as the threshold frequency, fT. The threshold frequency depends on the type of metal being exposed to the radiation. The photoelectric effect is, for all intents and purposes, an “all-or-nothing” response: if the frequency of the incident photon is less than the threshold frequency (f < fT),
then no electron will be ejected because the photons do not have sufficient energy to
dislodge the electron from its atom. But if the frequency of the incident photon is greater than the threshold frequency (f > fT), then an electron will be ejected, and the maximum kinetic energy of the ejected electron will be equal to the difference between hf and hfT (also called
the work function).
The energy of each photon is proportional
to the frequency of the light:
E = hf
Where E is the energy of the photon of light, h is Planck’s constant (6.626 × 10−34 J·s), and f is the frequency of the light.
Once we know the frequency, we can easily find the wavelength λ according to the equation c = fλ,
Kinetic energy of electron
Kmax = hf − W
where W is the work function of the metal in question. h = 6.626 × 10−34 J·s = 4.14 × 10−15 eV · s)
The work function is the minimum
energy required to eject an electron and is related to the threshold frequency of that metal by:
W = hfT
Mass defect
While one would assume that the mass of
the nucleus is simply the sum of the masses of all of the protons and neutrons within it, the actual mass of every nucleus (other than hydrogen) is slightly smaller than that. This
difference is called the mass defect.
E = mc^2
where E is energy, m is mass, and c is the speed of light. The mass defect is a result of matter that has been converted to energy.
Isotopic notation
When written in isotopic notation, elements are preceded by their atomic number as a
subscript and mass number as a superscript. The atomic number (Z) corresponds to
the number of protons in the nucleus; the mass number (A) corresponds to the number of protons plus neutrons.
Fusion, Fission.
Fusion occurs when small nuclei combine to form a larger nucleus
Fission is a process by which a large nucleus splits into smaller nuclei.
Isotope decay
Let the letters X and Y represent nuclear isotopes. When the parent nucleus X undergoes nuclear decay to form daughter nucleus Y, the balanced reaction is:
A X -> A Y + emitted decay particle
Z Z
When balancing nuclear reactions, the sum of the atomic numbers must be the same on both sides of equation, and the sum of the mass numbers must be the same on both sides as well.
Whenever you approach radioactive decay problems on the MCAT, start by balancing
the number of protons (the atomic numbers). Odten, wrong answer choices will simply
have an error in the number of protons and can be eliminated before even checking
the mass numbers.
Alpha decay
Alpha decay is the emission of an α-particle, which is a nucleus that consists of two
protons, two neutrons, and zero electrons. The alpha particle is very massive compared to a beta particle and carries double the charge. Alpha particles do not have any electrons, so they carry a charge of +2.
A X -> A-4 Y + 4 a
Z Z-2 2
Beta decay
Beta decay is the emission of a β-particle, which is an electron and is given the symbol e− or β−. Electrons do not reside in the nucleus, but they are emitted by the nucleus when a neutron decays into a proton, a β-particle.
In some cases of induced decay (positron emission), a positron is released, which has the mass of an electron but carries a positive charge. The positron is given the symbol e+ or β+.
In both types of beta decay, there needs to be conservation of charge. If a negative
charge (β−) is produced, a neutron is converted into a proton to maintain charge.
Conversely, if a positive charge (β+) is produced, a proton is converted into a neutron to maintain charge. Remember that negative beta decay produces a negative β-
particle and positive beta decay produces a positive β-particle.
A X -> A Y + 0 β−
Z Z+1 -1
Gamma decay
Gamma decay is the emission of γ-rays, which are high-energy (high-frequency) photons. They carry no charge and simply lower the energy of the parent nucleus without changing the mass number or the atomic number. high-energy state of the parent nucleus may be represented by an asterisk.
Gamma decay questions are the easiest on the MCAT. No changes occur in the mass
number or atomic number; only a γ-ray is emitted.
A X* -> A + γ
Z Z
Electron capture
Electron capture is a rare process
that is perhaps best thought of as the reverse of β− decay:
A X + e- -> A Y
Z Z-1
Half life
In a sample of radioactive particles, the half-life of the sample is the time it takes for
half of the sample to decay
Example:
If the half-life of a certain isotope is 4 years, what fraction of a sample of that
isotope will remain after 12 years?
Solution:
0-4 = 1/2
4-8= 1/2
8-12= 1/2
(1/2) ^3 = 1/8 because 3 half lives
