Briefly describe the Bohr Theory of the atom.
The Bohr Theory states:
- Electrons can only exist in fixed orbits or energy levels.
- These energy levels are at specific distances from the nucleus.
- Any energy emitted/absorbed from/by an atom will be the result of an electron jumping from one energy level to another.
In the Bohr Model, what does the hydrogen electron orbit?
The Bohr Model states that the hydrogen electron orbits the nucleus.
Note: all models assume that electrons orbit the nucleus, but Bohr's model is unique in that in most chemistry courses and on the AP Chemistry exam, the Bohr model is usually restricted to the hydrogen atom only.
In the quantum mechanical model, where does the hydrogen electron exist?
In a spherical probability cloud around the nucleus, called the 1s orbital.
Note: the quantum mechanical model is the one used in most chemistry courses and on the AP Chem exam.
An atomic electron has not absorbed any energy. Which state is it in?
The atomic electron is in the ground state.
The ground state is the lowest possible energy orbital that any atomic electron may occupy.
When a ground state hydrogen electron absorbs energy, what happens to it?
The hydrogen electron moves into an excited state.
Ex: a ground-state electron in hydrogen is in the 1s state. If it absorbs the right amount of energy, it can jump into the 3p state, which is excited (higher) in energy than the ground state.
What has to happen to an electron in order for it to change from the ground state to an excited state?
The electron must absorb energy, typically in the form of a photon, to go from the ground state to an excited state.
What direction does energy flow when an atomic electron drops from the excited state back to the ground state?
Energy is released from the atom.
Since the ground state is lower in energy than the excited state, the change from excited to ground is always accompanied by a release of energy from the atom.
The absorption spectrum is the unique set of wavelengths of light absorbed by a specific substance or medium.
The absorption spectrum is typically displayed as a set of dark lines (or missing lines) in the spectrum, representing the absorbed wavelengths. This is the third bar in the image.
The emission spectrum is the unique spectrum of bright lines or bands of light emitted by a particular substance when it is electronically excited.
This is the second bar in the image.
How do a substance's absorption and emission spectral lines compare to one another?
The absorption and emission spectral lines will overlap one another perfectly.
Both absorption and emission energy values are dependent on electrons moving between energy levels. Jumping to a higher level (dark absorption line) should be in the exact same position as jumping to a lower level (bright emission line) since it's the exact same amount of energy absorbed and emitted, respectively.
What is the quantum number n called?
n is the principal quantum number, and is commonly referred to as the shell the electron is in.
n can have any whole number value greater than or equal to 1.
As the principle quantum number n increases, what happens to the energy?
As n increases, energy increases.
Remember: assume that the quantum number l stays constant unless told otherwise.
What is the quantum number l called?
What does it represent?
l is the angular momentum (or azimuthal) number.
It represents an electron's subshell.
If l = 0, the electron is in an s subshell.
If l = 1, the electron is in a p subshell.
If l = 2, the electron is in a d subshell.
If l = 3, the electron is in a f subshell.
l can take any integer value from 0 to n - 1, but most chemistry courses and the AP Chem exam will only explicitly test 0 to 3.
In orbital theory, what do s, p, d, and f indicate?
How are these values determined?
The letters s, p, d, f symbolize the subshells in which an electron can exist.
The value of the quantum number l determines the subshell. s, p, d, and f subshells correspond to l = 0, 1, 2, and 3, respectively.
What is the quantum number m or ml called?
What does it represent?
m or ml is the magnetic quantum number.
It represents the orbital in which an electron exists.
m can hold any integer value between -l and +l, including 0.
Ex: for an electron whose l = 1 (p subshell), m can equal -1, 0, or 1. These values correspond to the px, py, and pz orbitals, respectively.
How many orbitals can be found in a p subshell?
A p subshell has three orbitals: px, py, and pz.
Remember: l = 1 for any p subshell. ml can range from -l to l (in this case: -1, 0, or 1) in a p subshell. These values correspond to the x, y, and z orbitals.
What is the quantum number s or ms called?
What does it represent?
s or ms is the spin quantum number.
It represents the spin direction of an electron.
s can have exactly one of two values, +1/2 and -1/2, corresponding to spin-up and spin-down. These two values are inherently equal in energy.
What is the value of l for any electron in an s orbital?
For any s electron, l = 0.
l can range from any value from 0 to n-1, and determines the subshell. By definition, if l = 0 for an electron, that electron exists in an s orbital.
What is the maximum number of electrons found in an orbital?
Each orbital can hold up to 2 electrons.
Note: When one orbital hold two electrons simultaneously, one must be spin-up and the other spin-down.
With 5 orbitals, how many electrons can a d subshell hold?
A d subshell holds up to 10 electrons.
Each of the 5 orbitals can have 1 spin-up electron and 1 spin-down, for a total of 2(5)=10 total.
s = 'spherical'
p = 'peanut'
d = 'donut'
How many electrons are there in a filled shell with principal quantum number n?
There are 2n2 electrons in the filled shell.
Ex: For the n = 2 shell:
2(22) = 8
This shell has 4 orbitals: 2s, 2px, 2py, 2pz. Each of those can hold 2 electrons, for a total of 8 in the shell.
How many orbitals are there per shell with principal quantum number n?
A shell will have n2 orbitals.
Ex: For the shell n = 2 there are 22 = 4 orbitals total. They are the 2s, 2px, 2py, and 2pz orbitals.
How many orbitals are there per subshell with azimuthal quantum number l?
A subshell will have 2(l) + 1 orbitals.
Ex: For a d subshell, l = 2, and there are 2(2) + 1 = 5 orbitals total. They are the dxy, dxz, dyz, dx2-y2, and dz2 orbitals.
An s subshell holds 1x2=2 electrons
A p subshell holds 3x2=6 electrons
A d subshell holds 5x2=10 electrons
An f subshell holds 7x2=14 electrons
Given two specific subshells, what determines which one will fill with electrons first?
The subshell with the lowest total energy will fill first.
Total energy can be approximated as E=n+l, where n=principal quantum # and l=azimuthal quantum #.
Ex: For a 4s subshell, n = 4 and l = 0, so n+l = 4. So a 4s subshell will fill before a 3d subshell, which has n = 3, l = 2, and n+l = 5.
Note: in the case of a tie between two subshells with the same n+l value, the one with the lower n will fill first.
Arrange the following subshells in terms of increasing energy:
4s, 6s, 3d, 2s, 4f
In order of increasing energy:
2s < 4s < 3d < 6s < 4f
The total order of all relevant subshells in the full Periodic Table is:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d
For a given value of n, please rank the following subshells in order of increasing energy:
p, s, f, d
In order of increasing energy:
s < p < d < f
These subshells differ in their value of l. For a given n, the higher the l, the higher the energy.
Explain each of the 3 terms for the spectroscopic notation for an atom's electronic structure?
Ex: the 3d5 depiction of Chromium's valence electrons.
The spectroscopic notation denotes the three most important pieces of information about a subshell: its energy level (n), subshell (l), and the total number of electrons it contains.
So Chromium's 3d5 explains that there are 5 valence electrons, with n = 3 and l = 2.
Give both the full and condensed form of the spectroscopic notation for Calcium (Ca).
The full electronic structure of Calcium is:
In condensed notation:
Since every up to 3p6 is completely filled, they are not chemically relevant - only valence electrons participate in chemical reactions. Therefore, they can all be abbreviated as the noble gas from the previous row, in this case Ar, which represents the element with fully-filled subshells up to 3p6.
the Aufbau Principle
The Aufbau Principle describes the order in which subshells are filled with electrons as atomic number increases. Aufbau is German for 'Building Up'.
Shells/subshells of lower energy get filled with electrons before higher energy shells/subshells.
Ex: The 1s subshell fills first, then 2s, then 2p, and so on.
Hund's Rules describe the order of adding electrons to an unfilled subshell.
Hund's Rules explain that when electrons are added to a subshell that has more than 1 orbital (p, d, or f), each orbital first receives a single electron, each spin-up, until each orbital in the subshell has one electron contained within it.
Only once the orbital is half full will spin-down electrons be added, one per orbital, until the subshell is completely filled.
the Pauli Exclusion Principle
The Pauli Exclusion Principle states that two electrons in the same orbital must be of different spins.
The result of this rule is that two electrons in the same atom will never have exactly the same 4 quantum numbers (n, l, ml, ms).
the Bohr Model of the hydrogen atom
The Bohr Model describes a hydrogen atom as a postively-charged nucleus which is orbited by a single electron. The electron can only exist in fixed energy orbits, called orbitals.
The differences in energy between orbitals are known as the energy levels of the hydrogen atom.
How can the possible energies of an electron in a hydrogen atom be calculated, according to the Bohr model?
The possible energies (En) of an electron in a hydrogen atom correspond to the formula:
En = -13.6/n2 eV
n is the principal quantum number of the orbital containing the electron.
Note: energy will necessarily be negative for all values of n.
How will energy vary as the value of n increases, according to the Bohr Model?
Energy increases as n increases.
En = -13.6/n2 eV
En is the energy of between nucleus and electron and will always be negative.Since n appears in the denominator, increasing n corresponds to the energy becoming less negative or more positive.
What is the equation for energy difference of an electron as it changes from an orbital with principal quantum number ni (initial) to nf (final), according to the Bohr Model?
The energy difference is:
ΔE = -13.6(1/nf2-1/ni2) eV
This shortcuts having to apply the Bohr Model energy formula to both orbitals and then subtract the initial energy from the final energy.
How much has energy increased, if an electron jumps from n=1 to n=2?
From ΔE = -13.6(1/nf2-1/ni2) eV
nf = 2, ni = 1, giving
ΔE = -13.6(1/22-1/12)
= -13.6(1/4 -1) = -13.6(-3/4)
= 10.2 eV
the emission spectrum of a hydrogen atom
Hydrogen's emission spectrum is the set of frequencies of light that a hydrogen atom can emit.
These particular frequencies are constant, and are uniquely characteristic of hydrogen.
Every element has a distinct emission spectrum; the presence of an element can be proven by observing its unique spectral lines.
How does the Bohr Model explain the frequency of the spectral lines in the emission spectrum of hydrogen?
Each emission spectral line is a result of the difference in energies between orbitals in the Bohr Model.
When an electron in a higher energy orbital falls into a lower energy orbital, it releases energy in the form of a photon. The frequency of the photon is determined by the difference in energy levels of the two orbitals. A large energy difference results in a higher photon frequency.
What are the characteristics of a proton?
A proton is a positively-charged subatomic particle.
Protons have mass of 1 AMU.
A proton is found inside the nucleus of an atom.
Protons contribute to the atomic mass and the atomic number.
What are the characteristics of a neutron?
A neutron is an uncharged subatomic particle.
Neutrons have mass of 1 AMU.
A neutron is found inside the nucleus of an atom.
Neutrons contribute to the atomic mass, but not the atomic number.
the atomic mass, A, of an atom
An atom's atomic mass corresponds to the sum of the neutrons and protons contained in the nucleus of that element.
The units of atomic mass are atomic mass units, AMU.
What is the atomic mass, A, of an atom of the standard isotope of oxygen?
The standard isotope of oxygen has 8 protons, and 8 neutrons, for a total of 16.
It is worth memorizing the atomic weights of some commonly-tested standard isotopes for the MCAT:
- A(H) = 1
- A(He) = 4
- A(C) = 12
- A(N) = 14
- A(O) = 16
- A(Na) = 23
the atomic number, Z, of an element
The atomic number of an element is the number of protons contained within the element's nucleus.
Atomic number is a characteristic property of an element. For instance, all atoms with 1 proton in their nucleus are hydrogen atoms, regardless of how many neutrons exist in the nucleus.
What is the atomic number, Z, of an atom of carbon?
Z(C) = 6
It is worth memorizing the following values of Z for the MCAT, as they are the most-commonly tested:
- Z(H) = 1
- Z(He) = 2
- Z(C) = 6
- Z(N) = 7
- Z(O) = 8
- Z(Na) = 11
- Z(Cl) = 17
A student doing tests on transition metals records the number 197 in their log book, but can't recall whether it was the A or Z value.
Which does it have to be?
197 must be the atomic mass (A).
There are only ~103 naturally ocuring elements, so the highest possible Z value for a natural element is 103.
What is the name for two atoms of the same element with different number of neutrons in their nuclei?
Atoms that differ only in their number of neutrons are called isotopes.
Isotopes have different masses, and can have different radioactive properties, but they are chemically identical.
What is the difference between an atom of carbon-12 and an atom of carbon-13?
C-12 and C-13 have different masses and number of neutrons.
An atom of carbon-12 has 6 protons and 6 neutrons in its nucleus, total mass 12. An atom of carbon-13 has 6 protons and 7 neutrons in its nucleus, total mass 13.
the nuclear force
The nuclear force holds protons and neutrons together in the nucleus.
In a very large atom, or one with an over-abundance of neutrons, the nucleus can become unstable and decay.
Which element is more likely to become unstable and decay, 21085Astatine or 5123Vanadium?
Astatine is more likely to have an unstable nucleus than vanadium.
Astatine coincidentally is radioactive, so matches the prediction perfectly.
The larger the nucleus, or greater number of neutrons, the more nuclear force is necessary to hold it together.
an alpha particle and alpha decay
An alpha particle is a helium nucleus, consisting of 2 protons and 2 neutrons (without the electrons).
Alpha decay is a nuclear decay and occurs when a nucleus emits an alpha particle.
The daughter nucleus of alpha decay will have an atomic number 2 less and mass number 4 less than the parent nucleus.
What will the daughter atom be when uranium-238 undergoes a single alpha decay?
In single alpha decay, an alpha particle is emitted. To identify the daughter nucleus: subtract 2 from the parent nucleus' atomic number, and 4 from its mass. Subtracting 2 protons from uranium (92) shifts it to thorium (90).
Under what conditions would alpha decay be an isotope's preferred form of radioactive decay?
Alpha decay is typical only in large nuclei (atomic number 60 or greater).
Many of the most well known radioactive elements, such as radium (88), uranium (92), and plutonium (94), decay primarily via alpha decay.
a beta particle and beta decay
A beta particle is an electron, a massless negatively-charged particle.
Beta decay is a nuclear decay and occurs when a nucleus emits a beta particle.
The daughter nucleus of beta decay will have an atomic number 1 greater and mass number identical to the parent nucleus. When the electron is ejected, total charge must remain constant, so a neutron is converted to a new proton.
What will the daughter atom be when carbon-14 undergoes a single beta decay?
In beta decay, a beta particle (electron) is emitted. To identify the daughter nucleus: add 1 to the parent nucleus' atomic number, without changing its mass. The element with an atomic number one larger than carbon is nitrogen.
Under what conditions is beta decay an isotope's preferred form of radioactive decay?
Beta decay is typical in smaller nuclei, when the isotope's mass number is greater than the element's atomic weight.
Ex: The carbon-16 isotope, is heavier than carbon's atomic weight of 12.011, and consequenly decays via beta decay.
a positron and positron decay
A positron is an anti-electron, a massless positively-charged particle.
Positron decay is a nuclear decay and occurs when a nucleus emits a positron.
The daughter nucleus of positron decay will have an atomic number 1 less and mass number identical to the parent nucleus. When the positron is ejected, total charge must remain constant, so a proton is converted to a new neutron.
What will the daughter atom be when carbon-11 undergoes positron decay?
In positron decay, a positron is emitted. To identify the daughter nucleus: subtract 1 from the parent nucleus' atomic number, without changing its mass. The element with an atomic number one less than carbon is boron.
Electron capture is a nuclear decay and occurs when a nucleus captures one of its own electrons. The electron merges with a proton to form a neutron.
The daughter nucleus of electron capture will have an atomic number 1 less and mass number identical to the parent nucleus.
What will the daughter atom be when beryllium-7 decays via electron capture?
In electron capture, an electron merges with a proton, forming a neutron. To identify the daughter nucleus: subtract 1 from the parent nucleus' atomic number, without changing its mass. The element with atomic number one less than beryllium is lithium.
Under what conditions would positron emission or electron capture be an isotope's preferred form of radioactive decay?
Both positron emission and electron capture are typical when the isotope's mass number is less than the element's atomic weight, or when there is a superabundance of protons.
Ex: The carbon-11 isotope, is lighter than carbon's atomic weight of 12.011, and consequently decays via positron emission.
a gamma ray and gamma emission
A gamma ray is a high energy photon, a massless and uncharged particle.
Gamma emission is a nuclear decay and occurs when a nucleus emits a gamma ray.
The daughter nucleus of gamma emission has only changed to lower energy, hence will have identical atomic and mass numbers to the parent nucleus.
the half-life of a radioactive isotope
A radioactive isotope's half-life is the time it takes for exactly one-half of the original isotope atoms to undergo radioactive decay.
After one half-life elapses, exactly one half of the original amount of the parent nuclei will still be present; the remainder will have decayed into the daughter nuclei.
What proportion of the original amount of radioactive isotope X will remain in 3 hours, if X has a half-life of 1 hour?
One-eighth of the original amount will remain after 3 hours.
For each half-life that elapses, one half of the remaining isotopes decays. After one hour, 1/2 the original population remains. During the second hour, 1/2 of the remaining half (1/4 more) decays, leaving one quarter of the original population. In the third hour, 1/2 of the remaining quarter (1/8 more) decays, leaving one eighth of the original.
How long will it take a 120 g sample of radioactive isotope Z to decay until only 30 g of Z remain, if Z has a half-life of 3 days?
For each half-life that elapses, one half of the remaining isotopes will decay. After 3 days, 60 g of Z will decay, and 60 g will remain. After 3 more days, half of that 60 g will decay, leaving 30 g.
Nuclear fission is a radioactive process in which a nucleus splits into two or more lighter nuclei.
Ex: an atom of 236U can fission into an atom of 92Kr, an atom of 142Ba, and 2 free neutrons.
Though this is a classic example, you do not need to memorize any specific fission reactions for the MCAT.
Nuclear fusion is a radioactive process in which two nuclei combine to form a heavier one.
Ex: an atom of 2H can fuse with an atom of 3H, forming an atom of 4He and a free neutron, along with significant excess energy.
Though this is a classic reaction (in the sun), you do not need to memorize any fusion reactions for the MCAT.
mass defect of an atom
An atom's mass defect is the difference between the calculated mass of the individual protons and neutrons in the atom's nucleus compared to the overall observed mass of the nucleus.
The mass defect is due to some mass being converted to energy to hold the nucleus together. The nucleus will consequently weigh less than the protons and neutrons that make it up.
binding energy of a nucleus
The binding energy of a nucleus is the energy needed to cause the nucleus to decompose into separate protons and neutrons.
The binding energy is exactly the same magnitude as the mass defect. The energy released when a nucleus is formed is exactly the same as the energy needed to break it apart.
What is the equation relating a nucleus' mass defect and its binding energy?
E = mc2
E = nucleus' binding energy
m = nucleus' mass defect
c = speed of light, 3x108 m/s
Since the value of c2 is so large, a very small mass defect accounts for a very large binding energy.
The mass of 2 free protons and 2 free neutrons is about 4.032 AMU, but the mass of an alpha particle is about 4.002 AMU. What explains the discrepancy?
The remaining 0.030 AMU is the binding energy of the alpha particle.
Remember: the binding energy is the mass converted to energy when the nucleus is formed.
Using E = mc2, 0.030 AMU corresponds to 28.3 MeV of energy.
The binding energy of an alpha particle is 28.3 MeV. How much energy is needed to separate an alpha particle into its consitutent pieces?
28.3 MeV is the energy required to break apart the alpha particle.
Remember: the binding energy is the mass converted to energy when the nucleus is formed. That much energy is required to break the nucleus apart.