Lesson 1: Atomic Mass and Exponential Decay

Question 1

Correctly match the following terms with their abbreviation:

I. Mass number
II. Atomic number
III. Number of neutrons

(A) A
(B) M
(C) N
(D) Z

Answer 1

Question 2

Hydrogen has an atomic number of 1 and an atomic mass of 1. Deuterium has an atomic number of 1 and an atomic mass of 2. How many protons does Hydrogen have compared with Deuterium?

Answer 2

Hydrogen has 1 proton as its atomic number is 1.

Deuterium also has 1 proton as its atomic number is also 1.

Question 3

What is responsible for the extra mass within Deuterium as compared to Hydrogen?

Answer 3

Deuterium has an extra neutron compared to Hydrogen.

Question 4

Deuterium and Hydrogen are related in that they are:

(A) Isomers
(B) Isotropes
(C) Isotonic compounds
(D) Isotopes

Answer 4

(D) Isotopes

Isotopes are similar in atomic number but different in terms of their atomic mass, due to differing numbers of neutrons.

Question 5

An atom with an atomic mass of 161 and 87 neutrons is an isotope of what element? (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)

(A) Francium
(B) Dysporium
(C) Terbium
(D) Tungsten

Answer 5

(D) Tungsten

161 neutrons and protons - 87 neutrons = 74 protons

Consulting the periodic table, the element with 74 protons is Tungsten (W).

Question 6

Uranium has an atomic number of 92 and an atomic mass of 235. How many neutrons does Uranium contain?

(A) 92
(B) 110
(C) 143
(D) 235

Answer 6

(C) 143

235 neutrons and protons - 92 protons = 143 neutrons

Question 7

Compare atomic mass and atomic weight.

Answer 7

The atomic mass of an atom is a discrete number based on the number of nucleons in a single atom.

The atomic weight of an element is a weighted average of the atomic masses of all atoms of that element in nature.

Question 8

Why is the atomic weight of Carbon reported as 12.01 instead of 12?

Answer 8

Because not all Carbon in nature is the Carbon-12 isotope. You have to account for the Carbon-13 that exists out there. The atomic weight is a weighted average

Question 9

What percent of Carbon atoms out there are Carbon-12 if the atomic weight of Carbon is 12.01?

Answer 9

About 99 percent of Carbon in nature is Carbon 12.

Question 10

What percentage of Chlorine atoms are Chlorine-35 (34.97 amu) and Chlorine-37 (36.97 amu) if these are the only two isotopes that exist and the atomic weight is 35.45 amu?

(A) 26.58% Chlorine-35; 74.42% Chlorine-37
(B) 50.35% Chlorine-35; 49.65% Chlorine-37
(C) 75.77% Chlorine-35; 24.23% Chlorine-37
(D) 90.21% Chlorine-35; 9.79% Chlorine-37

Answer 10

(C) 75.77% Chlorine-35; 24.23% Chlorine-37

34.97(x) + 36.97 (1-x) = 35.45

2x = 1.52
x = 0.76 = 76%

Approximately 75% of the chlorine is Chlorine-35 and 25% is Chlorine-37.

Question 11

What accounts for the actual mass of Helium being .03 amu less than its predicted mass (the mass expected based on the individual masses of its protons, neutrons and electrons)?

Answer 11

The .03 amu is a result of the mass being converted into energy as the protons, neutrons, and electrons are brought together to form the atom.

Question 12

The actual mass of Helium is .03 amu less than its predicted mass (the mass expected based on the individual masses of its protons, neutrons and electrons). In the case of Helium, .03 amu is considered the:

(A) Binding energy
(B) Atomic mass
(C) Atomic mass difference
(D) Mass defect

Answer 12

(D) Mass defect

The mass defect is the mass difference between the actual and predicted mass of an atom.

Question 13

What equation for energy equates a change in mass to a change in energy?

Answer 13

E= mc^2

E = Energy
m = mass
c = speed of light = 3⋅10^8 m/s

Question 14

If there is a 0.03 amu mass defect of Helium, there are 1.66054 ⋅ 10^-27 kg per amu, and the speed of light is 2.99792 ⋅ 10^8, what is the binding energy for Helium?

(A) 1.2 ⋅ 10^-6 J
(B) 5.8 ⋅ 10^-9 J
(C) 4.5 ⋅ 10^-12 J
(D) 9.4 ⋅ 10^-14 J

Answer 14

(C) 4.5 ⋅ 10^-12 J

(.03 amu )⋅(1.66054 ⋅ 10^-27 kg/amu) = 5 ⋅ 10^-29 kg

E = mc^2
E = (5 ⋅ 10^-29)((3 ⋅ 10^8)^2)
E = 4.5 ⋅ 10^-12 J

Question 15

What is Avogadro’s number equal to, and how does it relate the number of atoms of an element to moles?

Answer 15

Avogadro’s number (NA)= 6.02 ⋅ 10^23 mol^-1
Avogadro’s number is the number of atoms/molecules in a mole, so multiplying Avogadro’s number by the moles of an element gives the number of atoms of that element.

Question 16

If the atomic weight of Xenon is 131.3, how much does 10^22 atoms of Xenon weigh in grams?

(A) 1.31 g
(B) 2.18 g
(C) 4.97 g
(D) 11.31 g

Answer 16

(B) 2.18 g

10^22/(6.02 ⋅ 10^23 mol^-1) = approx 1.5 ⋅ 10^-2 mol (actual 0.0166 mol Xenon)

0.0166mol ⋅ 131.3 g/mol = approximately 2.5g Xenon (actual 2.18g Xenon)

Question 17

The nuclear strong force accounts for what phenomenon?

Answer 17

The nuclear strong force accounts for the fact that the protons in the nucleus are both positively charged and yet are not repelling each other.

Question 18

Which of the following are considered nucleons?

I. Protons
II. Neutrons
III. Electrons

(A) I Only
(B) I and II Only
(C) II and III Only
(D) I, II, and III

Answer 18

(B) I and II Only

Protons and neutrons are both considered nucleons as they are both found in the nucleus of an atom.

Question 19

When describing the mass number of an atom, the units used are __________. One of these units can describe the mass of ____________.

(A) amu, protons
(B) amu, neutrons
(C) amu, nucleons
(D) grams, neutrons

Answer 19

(C) amu, nucleons

When describing the mass number of an atom, the units used are atomic mass units (amu). One of these units can describe the mass of nucleons (both protons and neutrons).

Question 20

True or false? Although not a nucleon, an electron’s mass is also approximately 1 amu.

Answer 20

False. An electron’s mass is about 1/2000th of an amu, making it significantly less massive than a nucleon.

Question 21

Which is stronger? The electrostatic force between the protons in a nucleus, or the nuclear strong force?

Answer 21

The nuclear strong force, which is why the protons are not repelled away from each other.

Question 22

Which only acts over short distances? The electrostatic force between the protons in a nucleus, or the nuclear strong force?

Answer 22

The nuclear strong force only acts over short distances.

Question 23

The N/Z ratio of Carbon-14 is 4/3. What does this indicate concerning the stability of Carbon-14?

Answer 23

It is unstable and will undergo radioactive decay.

Question 24

The stable N/Z ratio for large atoms (Z > 83) is greater or less than that of small atoms? Why?

Answer 24

The stable N/Z ratio for large atoms is greater than that of small atoms. This is due to the fact that once you add more nucleons to a nucleus, the protons on opposite ends of the nucleus will not experience the strong nuclear force; thus, protons will be more repelled from one another, resulting in less protons per neutrons in the nucleus.

Question 25

Carbon-14 undergoes radioactive decay, forming Nitrogen-14 and what other particle? This is an example of?

(A) Positron, positron emission
(B) Alpha particle, alpha-decay
(C) Electron, beta-decay
(D) Photon, gamma-decay

Answer 25

(C) Electron, beta-decay

Carbon-14 would emit an electron, resulting in the conversion of one neutron into a proton.

Question 26

Uranium-238 undergoes radioactive decay, forming Thorium-234 and what other particle? This is an example of?

(A) Positron, positron emission
(B) Alpha particle, alpha-decay
(C) Electron, beta-decay
(D) Photon, gamma-decay

Answer 26

(B) Alpha particle, alpha-decay

Question 27

Technitium-99 undergoes radioactive decay, forming Technitium-99 (with the same number of protons) and what other particle? This is an example of?

(A) Positron, positron-emission
(B) Alpha particle, alpha-decay
(C) Electron, beta-decay
(D) Photon, gamma-decay

Answer 27

(D) Photon, gamma-decay

Question 28

Berylium-7 undergoes radioactive decay, forming Lithium-7 (Berylium-7 with one less proton and one more neutron) and what other particle? This is an example of?

(A) Positron, positron-emission
(B) Alpha particle, alpha-decay
(C) Electron, beta-decay
(D) Photon, gamma-decay

Answer 28

(A) Positron, positron-emission

Question 29

Electron capture is another form of radioactive decay, where a proton is converted to a neutron. Electron capture could be considered the reverse process of which aforementioned radioactive decay type?

(A) Positron emission
(B) Alpha-decay
(C) Beta-decay
(D) Gamma-decay

Answer 29

(C) Beta-decay

In Beta-decay, a neutron is split into a proton and an electron that is emitted.

In Electron capture, an electron is taken into the nucleus to turn a proton into a neutron.

Question 30

A positively charged atom is called a _________, whereas a negatively charged atom is called a ____________.

(A) Positron, electron
(B) Cation, anion
(C) Anion, cation
(D) Electron, positron

Answer 30

(B) Cation, anion

A positively charged atom is called a cation, whereas a negatively charged atom is called a anion.

Question 31

True or false? A formerly neutral Carbon-14 undergoes beta-decay to become the anion Nitrogen-14.

Answer 31

False. A formerly neutral Carbon-14 undergoes beta-decay to become the CATION Nitrogen-14.

Question 32

Which of the following is an anion? (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)

(A) Krypton-85 with 36 electrons
(B) Vanadium-45 with 21 electrons
(C) Cadmium-111 with 50 electrons
(D) Bromine-79 with 34 electrons

Answer 32

(C) Cadmium-111 with 50 electrons

Cadmium has 48 protons, so (C) is an anion.
Krypton has 36 protons, so (A) is neutral.
Vanadium has 23 protons, so (B) is a cation.
Bromine has 35 protons, so (D) is a cation.

Question 33

Which type of particles are most often involved in creating bonds between multiple atoms, since they have the weakest interactions with the nucleus?

(A) 1s electrons
(B) Neutrons
(C) Valence electrons
(D) Positrons

Answer 33

(C) Valence electrons

Because valence electrons are furthest from the nucleus, they have the weakest interactions with the nucleus, the strongest interactions with the environment, and they often form bonds between atoms.

Question 34

Explain the term “half-life” and the shape of a half-life plot.

Answer 34

The half-life of a sample is how long it takes for half of the sample to decay. A half-life plot is a hyperbolic curve with an asymptote at y=0.

Question 35

The half-life of Carbon 14 is 5,740 years. If you have 37 grams of Carbon-14, approximately how much Carbon will be left after 14,304 years?

(A) 4.875 grams
(B) 6.73 grams
(C) 10.43 grams
(D) 17.34 grams

Answer 35

(B) 6.73 grams

Approximation can be used to quickly find this answer.

(0 half-lives) At 0 years -> 37 grams
(1 half-lives) After 5,740 years -> 18.5 grams
(2 half-lives) After 11,480 years -> 9.25 grams
(3 half-lives) After 17,220 years -> 4.625 grams

Since 14,304 years is about 2.5 half-lives, the best answer choice is (B) 6.73 grams.