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Chemistry I Lesson I: Atomic Mass and Exponential Decay

Terms in this set (102)

For the atom carbon, which has a value of 6?

a. number of valence electrons
b. mass number (A)
c. atomic mass
d. atomic number (Z)
d. atomic number (Z)
Which of the following defines an element?

a. atomic mass
b. atomic number (Z)
c. number of valence electrons
d. number of total electrons
b. atomic number (Z) (i.e. number of protons)
Describe the two pieces of information that are usually explicitly provided for each element on a periodic table.
1. atomic number (Z) = number of protons, it defines an element

2. atomic weight = the weighted average mass of the isotopes of an element, measured in amu
What piece of information defines the isotope of an element?
mass number (A)
For a given isotope, the superscript tells you the a)__________ and the subscript tells you the b)__________?
a) mass number (A), defines isotope
b) atomic number (Z), defines element
Protium, deuterium, and tritium are all examples of what? What are their similarities and differences?
They are isotopes of hydrogen. Isotopes have the same atomic number because they are the same element. Therefore the isotopes of hydrogen all have the same atomic number (Z) = 1, which is equal to the number of protons for hydrogen. They all contain a different number of neutrons, making them isotopes of one another. Protium has zero neutrons, so its mass number is 1. Deuterium has one neutrons so its mass number is 2. Tritium has two neutrons so its mass number is 3. The prefix of the isotope refers to the number of "things" in the nucleus of the atom.
What is an equation to represent the mass number?
A = Z + N

mass number = atomic number + number of neutrons
What is an equation to represent the number of neutrons in an atom?
N = A - Z

number of neutrons = mass number - atomic number
What is another name for hydrogen-3?
tritium
How many neutrons are in carbon-12 and what does the 12 represent?
The 12 represents the mass number (A), which defines the isotope of carbon. In this case carbon has 6 protons and 6 neutrons because N = A - Z, so N = 12 - 6, which equals 6.
What is the difference between hydrogen-1 and hydrogen-2?
They are isotopes of one another. Hydrogen-1 has a mass number of 1 and contains 1 proton and 0 neutrons. Hydrogen-2 has a mass number of 2 and contains 1 proton and 1 neutron.
How do scientists define an amu?
Mass of carbon-12 = 12 amu
What is the approximate value of one amu in kg?
1 amu = 1.7 x 10^-27 kg
What is atomic mass?
weight of one atom, which is very close to the mass number
Why is the mass number so close to the atomic mass?
Because 1) electrons have negligible mass, so the nucleus (protons and neutrons) comprise all the mass of an atom and 2) protons and neutrons both have a mass of roughly 1 amu
Do protons and neutrons have the same mass?
Very very close to the same mass. A proton has a mass of roughly 1.007 amu and a neutron has a mass of 1.009 amu. A neutron is ever-so-slightly more massive.
True or false: the atomic weight is measured in amu and provides the mass of the single most abundant isotope of an element.
False. It is measured in amu, but it comprises the weighted average mass of all the isotopes of the given element.
True or false? The atomic mass is a prediction of the mass of an atom.
True.
How does the predicted atomic mass differ from the actual atomic mass?
Predicted atomic mass > actual atomic mass
What is mass defect?
Mass defect is the difference between the predicted atomic mass and the actual atomic mass.

mass defect = predicted atomic mass - actual atomic mass
What causes mass defect?
The important physical principal at play is that mass and energy can interconvert! Some atomic mass is "lost" when a nucleus is formed because it is converted to energy that is released from the nucleons
How does mass defect relate to nuclear binding energy?
The mass defect is converted to energy, which is "released" when the nucleus is formed. This energy is called the nuclear binding energy.
What equation relates mass and energy?
E = mc^2
What are the steps to solving for the nuclear binding energy?
1. Solve for mass defect by subtracting actual atomic mass from predicted atomic mass.
2. Convert mass defect from amu to kg.
3. Use E = mc^2 to solve for binding energy (in Joules)
What happens when nuclear binding energy is released from nucleons?
A nucleus is formed
What happens when nuclear binding energy is consumed by nucleons?
A nucleus breaks apart
Why don't the positive charges in the nucleus repel one another?
The nuclear strong force holds the positive charges together
Does a stable nucleus or separated nucleus have more mass? Why?
A separated nucleus has more mass because a stable nucleus loses some mass when it is converted to the nuclear binding energy
How does the nuclear strong force compare to the electrostatic force that acts to push the protons in a nucleus away from one another?
The nuclear strong force is MUCH stronger than the electrostatic force, which is why the nucleus does not spontaneously break apart

Nuclear strong force > electrostatic force
Why don't we see nuclear strong force acting on everyday objects?
Because nuclear strong force only occurs at VERY small distances
What is the relationship between the nuclear strong force and nuclear binding energy?
The nuclear binding energy is the amount of energy needed to overcome the strong force and break a nucleus apart. Different units! Force=N. Energy= Nm (J).
Is there a difference between binding energy and nuclear binding energy?
No, different ways to say the same thing
Nucleons are (select all that apply):

I. protons
II. neutrons
III. electrons
I and II
What is the rest mass energy and how do you calculate it?
The amount of energy contained in a resting object of given mass. Use E=mc^2. Make sure the mass is in kg.
rest mass energy (RME) atom + BE = ?
RME protons + RME neutrons + RME electrons
How do you solve for BE using rest mass energies (RMEs)?
BE = sum RME constituent parts - RME atom
What is BE measured in
unified amus ("u")
Is breaking a nucleus into its constituent parts endergonic or exergonic and why?
It is endergonic because it requires energy (the nuclear binding energy).
Is forming a nucleus from its constituent parts endergonic or exergonic and why?
It is exergonic because it releases energy (the nuclear binding energy).
What does the energy-mass equivalence show?
It shows that mass is just another form of energy
How did Einstein derive the mathematical formula for the energy mass equivalence?
He derived it from the kinetic energy of an object
What is the formula that represents energy mass equivalence?
E=mc^2
What does the variable E represent in the formula E=mc^2 and what are its SI units?
The rest mass energy (in Joules)
What happens if you combine an electron and a positron?
Gamma radiation- their masses combine and then disappear and release electromagnetic radiation (light) in the process
From what kind of energy can you produce electrons under lab conditions?
Electromagnetic radiation can produce electrons and other subatomic particles
What is happening in the sun when it produces electromagnetic radiation?
Subatomic masses combine and disappear, releasing electromagnetic radiation in the process. This means that the sun is constantly losing mass. This is an example energy mass equivalence in action.
What are two different ways to describe the nuclear binding energy?
1) It is the amount of energy required to break a nucleus into its nucleons/amount of energy released when nucleons come together to form a nucleus

2) It is the energy that holds the nucleus together, and the sum of the nuclear strong forces
What happens to atoms with unstable nuclei?
They undergo spontaneous radioactive decay
What kind of collision is radioactive decay?
Reverse completely inelastic collisions
What are the rules for stable nuclei for the three Z ranges?
Z≤20, stable if N/Z=1
20<Z≤83, stable if N/Z=1.5
83<Z, never stable
Why does the N/Z ratio of stable nuclei increase as Z increases?
The distances between protons and neutrons in the nucleus increases, so the net strong force can no longer act to hold them together. Electrostatic force can now push them apart.

Therefore, neutrons are needed to increase the sum of nuclear strong forces and overcome the electrostatic force.
What are four values that relate to how stable a nucleus is?
1. Number of protons
2.Neutron to proton (N/Z) ratio
3. Rate of radioactive decay (represented by decay constant/alpha)
4. Half-life
What is one value that is inversely proportional to how unstable a nucleus is?
Half-life
Name five types of radioactive decay
1. Alpha decay
2. Beta decay
3. Electron capture
4. Positron emission
5. Gamma decay
What two things are conserved in a nuclear equation?
The number of nucleons, which is the mass number (A) AND the charge of the nucleus
True or false: nuclei with Z>83 must maintain an N/Z ratio of 3 to remain stable.
False. These nuclei will always be unstable and will undergo radioactive decay.
What happens during alpha decay?
An alpha particle (helium nucleus or helium ion of +2 charge) is ejected from the nucleus.

Net loss of two neutrons and two protons (loss of 4 nucleons).

Move two to the left on the periodic table.
Write an equation for alpha decay of Radon-198
198/86 Rn (Radon 198) --> 4/2 He (alpha particle) + 194/84 Po (Polonium-194)
What is occurring during the following process?

U-238 --> Th-234
4 nucleons are lost (two protons, which converts Uranium to Thorium and two neutrons).

Therefore this is alpha decay of Uranium.

238/92 U --> 4/2 He + 234/90 Th
What happens during beta decay?
A beta particle (electron) is ejected from the nucleus.

A neutron turns into a proton and an electron.

Net gain of one proton and loss of one neutron (no change in number of nucleons).

Move one to the right on the periodic table.
Write an equation for what is happening to a neutron during beta decay
1/0 n (neutron) --> 0/-1 e (electron) + 1/1 p (proton)
What kind of atoms undergo beta decay?
Atoms with too many neutrons (i.e. a high N/Z ratio)
What force governs beta decay?
Nuclear weak force
Why and how does carbon-14 undergo spontaneous nuclear decay?
Because N/Z = 8/6, which is > 1 so it is not stable.

It undergoes beta decay to convert a neutron to a proton and electron:
14/6 C (Carbon-14) --> 0/-1 e (electron) + 14/7 N (Nitrogen-14) to get N/Z = 7/7 = 1.
Why and how does Th-234 undergo beta decay?
Because Z> 83 and N/Z= 144/90 so there are a lot of neutrons and protons.

It can convert a neutron to a proton and electron:
234/90 Th --> 0/-1 e + 234/91 Pa

Or lose two protons and two neutrons in alpha decay
Is Phosphorus-32 stable?
Z=15, so in order to be stable it must have N/Z ratio of 1

Its N/Z ratio is 17/15 = 2.13, which is high, indicating too many neutrons in its nucleus

Therefore it is not stable and will undergo beta decay to turn a neutron into a proton and electron
Write an equation for beta decay of Phosphorus-32
32/15 P --> 0/-1 e (beta particle) + 32/16 S (Sulfur-32)
What happens during positron emission?
A positron is ejected from the nucleus.

A proton turns into a neutron and a positron.

Net loss of one proton and gain of one neutron (no change in number of nucleons).

Move one to the left on the periodic table.
What kind of atoms undergo positron emission?
Atoms with too many protons (i.e. a low N/Z ratio)
Write an equation for what is happening to a nucleus during positron emission
1/1 p (proton) --> 0/1 e (positron) + 1/0 n (neutron)
Why would Carbon-11 undergo positron emission?
Its N/Z ratio is 5/6, which is low, indicating too many protons in its nucleus.

It will undergo positron emission to turn a proton into a positron and neutron.
What happens during electron capture
A neutron is created in the nucleus.

An electron and a proton turn into a neutron.

Net loss of one proton and gain of one neutron (no change in number of nucleons). Same net effect as positron emission.

Electromagnetic radiation is released (gamma radiation; 0/0 gamma)
Write an equation for what is happening to the nucleus during electron capture
0/-1 e + 1/1 p (proton) --> 1/0 n (neutron) + 0/0 gamma
What happens during gamma decay?
A gamma ray is ejected from the nucleus.

Mass turns into energy.

Net loss of mass gain of energy.

No change in the element.
Write an equation for what is happening in the nucleus during gamma decay
0/1 e (positron) + 0/-1 e (electron) --> 0/0 gamma + 0/0 gamma
Write an equation for gamma decay of Technetium-99* (excited Tc-99)
99/43 Tc* (excited state Tc-99) --> 0/0 gamma (gamma energy) + 99/43 Tc (ground-state Tc-99)
What does the half-life represent?
The amount of time that 50% of the nuclei of a population of atoms will decay assuming the law of large numbers
What value does half-life depend on?
Decay constant (alpha)
Write an equation for the number of atoms that have not decayed in terms of decay constant, half-life, and number of initial atoms
N = Nø • e^(-alpha)(t)

Nø = initial number of atoms
alpha = decay constant (varies inversely with half-life)
t= time gone by
Exponential decay graph!
Write an equation that represents the half-life in terms of the decay constant
t 1/2= ln(2)/alpha

t 1/2= half-life
alpha = decay constant
What is the mathematical relationship between the half-life and decay constant?
half-life and decay constant are inversely proportional
How does half-life relate to instability of a nucleus?
Inversely proportional:
As instability increases, half-life decreases

As instability decreases, half-life increases
How does decay constant relate to instability of a nucleus?
Proportional:
As instability increases, decay constant increases

As instability decreases, decay constant decreases
What is transmutation?
The conversion of one element or isotope to another element or isotope
All of the following are examples of transmutation EXCEPT

I. The beta decay of Carbon-14 to Nitrogen-14
II. The conversion of one isotope to another isotope of the same element
III. The conversion of oxygen and glucose to carbon dioxide and water

a. II and III
b. I
c. II
d. III
d. III
When does radioactive decay occur?
When a nucleus has a higher energy level than the nucleus into which it might decay
What is is the difference between energy of initial nucleus and energy of nucleus after radioactive decay called and is it released or absorbed during radioactive decay?
Ionization radiation and it is released during radioactive decay because a nucleus is going from higher energy to lower energy, which is an exergonic process
Why is it called ionization radiation?
Because radioactive decay produces ions. These charges are omitted in radioactive equations to highlight what is going on in the nucleus. Also these ions are usually quickly neutralized.
Rank the energy of radioactive particles emitted from low to high
alpha < beta < gamma (electromagnetic radiation that is higher in energy than UV)
What types of EM radiation can an excited electron returning to ground state emit and rank the energy of each form from high to low.
gamma > xrays > UV > visible light
What causes atoms to have electrons in a higher, unstable, excited state?
If they are the products of radioactive decay

If they get bombarded with radiation from other reactions
What are two other types of radioactivity, besides radioactive decay?
Spontaneous fission and fusion
What is Avagadro's number?
NA = 6.023 x 10^23 molecules/mole
What is the mass number?
Number of protons and neutrons of a given atom
True or false. Atomic mass is the same as mass number.
For our purposes true. But technically false. Atomic mass would take into account the mass of the electrons and the slight variation between mass of neutrons and protons. Mass number is equal to the number of nucleons, which is usually very close to the atomic mass so can treat them the same on the MCAT unless otherwise stated.
True or false. Atomic mass is the same as atomic weight.
False. Atomic mass is the mass of one kind of atom/isotope, whereas atomic weight is a weighted average mass of an element
What is atomic weight?
The weighted average of the atomic masses of all naturally occurring isotopes of an element
What is the conversion factor to go from amu to kg?
1.7 x 10^-27 kg/ 1 amu
What is the speed of light?
c = 3x10^8 m/s
What is the atomic mass of carbon-12?
12.00 amu
What is the atomic mass of carbon-13?
13.003 amu
What are the units for atomic mass and atomic weight?
amu
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