Nuclear & Atomic Phenomena

Question 1

What features characterize a proton?

Answer 1

A positively-charged subatomic particle with a mass of 1 amu.

Protons are found inside the nuclei of atoms. They contribute to both the atomic mass and the atomic number.

Question 2

What features characterize a neutron?

Answer 2

An uncharged subatomic particle with a mass of 1 amu.

Neutrons are found inside the nuclei of atoms. They contribute to the atomic mass, but not the atomic number.

Question 3

Define:

atomic mass

Answer 3

The sum of the neutrons and protons contained in its nucleus.

Atomic mass is measured in amu, or atomic mass units. It is often denoted as simply “A.”

Question 4

What is the atomic mass of an atom of the standard isotope of oxygen?

Answer 4

An atom of oxygen has a mass of 16 amu.

The standard isotope of oxygen has 8 protons and 8 neutrons, for a total of 16 nucleons. Note that for the MCAT, it is helpful to have some common atomic weights memorized. Namely, oxygen weighs 16 amu, nitrogen weighs 14 amu, and carbon weighs 12 amu. This information can also be found on the periodic table.

Question 5

Define:

atomic number

Answer 5

The number of protons contained within its nucleus.

Atomic number is a characteristic property of an element. For instance, any atom with one proton in its nucleus is a hydrogen atom, regardless of its number of neutrons. Atomic number is often denoted as “Z.”

Question 6

What is the atomic number of an atom of carbon?

Answer 6

6

In other words, carbon atoms contain 6 protons.

While multiple isotopes of carbon exist, they differ in their number of neutrons, not protons.

Question 7

A student testing a transition metal records the number 197 in his log book, but can’t recall whether it was the A or Z value. Which does it have to be?

Answer 7

197 must be the atomic mass, or A value.

There are approximately 103 naturally occurring elements, so the highest possible Z value for a natural element is 103. No known element has 197 protons.

Question 8

What term is used for two atoms of the same element that contain different numbers of neutrons?

Answer 8

Atoms that differ only in their number of neutrons are called isotopes.

Isotopes have different masses and can have different radioactive properties; however, they are chemically identical.

Question 9

What is the difference between an atom of carbon-12 and an atom of carbon-13?

Answer 9

• C-12 and C-13 have different atomic masses.
• They also differ in their number of neutrons.

An atom of carbon-12 has 6 protons and 6 neutrons in its nucleus, for a total mass of 12 amu. An atom of carbon-13 has 6 protons and 7 neutrons in its nucleus, for a total mass of 13 amu.

Question 10

Define:

nuclear force

Answer 10

A short-range attractive force that holds protons and neutrons together in the nucleus.

In a very large atom, or in one with an overabundance of neutrons, the nucleus can become unstable and decay. In such cases, the nuclear force is not sufficient to hold the nucleons together.

Question 11

Which element is more likely to spontaneously decay, ²¹⁰₈₅Astatine or ⁵¹₂₃Vanadium?

Answer 11

Astatine is more likely to decay than vanadium.

The larger the nucleus, and the greater the number of neutrons, the more nuclear force is required to hold the nucleons together. Astanine has significantly more neutrons than vanadium and would decay much more readily.

Question 12

An alpha particle is composed of the nucleus of which element?

Answer 12

A helium nucleus, consisting of two protons and two neutrons.

Note that, as a nucleus alone, an alpha particle does not contain electrons.

Question 13

Define:

alpha decay

Answer 13

A form of radioactive decay in which a nucleus emits an alpha particle, or helium nucleus.

The daughter nucleus produced from an alpha decay will have an atomic number two less, and a mass number four less, than the parent nucleus.

Question 14

What daughter atom will be produced when uranium-238 undergoes a single alpha decay?

Answer 14

²³⁴₉₀Th

In a single alpha decay, one alpha particle is emitted. To identify the daughter nucleus, subtract two from the parent nucleus’ atomic number and four from its atomic mass. Subtracting two protons from uranium, which had 92, shifts it to thorium, which has 90.

Question 15

Under what conditions would an isotope preferentially undergo alpha decay?

Answer 15

Alpha decay is typical only in large nuclei.

On the MCAT, it will likely only be undergone by elements with atomic numbers of 60 or greater.

Many of the most well-known radioactive elements, such as radium (88 protons), uranium (92 protons), and plutonium (94 protons), decay primarily via alpha decay.

Question 16

A beta particle is known by what other name?

Assume that this question refers to ß^- decay.

Answer 16

An electron, a negatively-charged particle with an extremely small (essentially negligible) mass.

If this question were referring to ß⁺ decay, the particle involved would be a positron.

Question 17

Define:

beta decay

(ß^- decay)

Answer 17

A form of radioactive decay in which a nucleus emits a beta particle, or electron.

The daughter nucleus of beta decay will have an atomic number one greater than, and a mass number identical to, the parent nucleus. It involves an existing neutron being converted to a proton. When the MCAT mentions beta decay, it is referring to this process unless it explicitly mentions otherwise.

Question 18

What daughter atom will be produced when carbon-14 undergoes a single beta decay?

Answer 18

¹⁴₇N

In a single beta decay, one beta particle, or electron, is emitted.

To identify the daughter nucleus, add one to the parent nucleus’ atomic number without changing its atomic mass. The element with an atomic number one greater than carbon is nitrogen.

Question 19

Under what conditions would an isotope preferentially undergo beta decay?

Answer 19

Beta decay is typical in smaller nuclei, usually when the isotope’s mass number is greater than the element’s atomic weight.

One example is the carbon-16 isotope. This nucleus is heavier than carbon’s usual atomic weight of 12.011 and consequently undergoes beta decay.

Question 20

What mass and charge do positrons have?

Answer 20

A positively-charged particle with an extremely small (essentially negligible) mass.

It is the positive counterpart of an electron.

Question 21

Define:

positron emission

(ß⁺ decay)

Answer 21

A form of radioactive decay in which a nucleus emits a positron.

The daughter nucleus of positron decay will have an atomic number one less than, and a mass number identical to, the parent nucleus. It involves an existing proton being converted to a neutron.

Question 22

What daughter atom will be produced when carbon-11 undergoes positron emission?

Answer 22

¹¹₅B

In positron decay, a positron is emitted from the atom. To identify the daughter nucleus, subtract one from the parent nucleus’ atomic number without changing its atomic mass. The element with an atomic number one less than carbon is boron.

Question 23

Define:

electron capture

Answer 23

A form of radioactive decay in which 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 one less than, and a mass number identical to, the parent nucleus.

Question 24

What daughter atom will be produced when beryllium-7 decays via electron capture?

Answer 24

⁷₃Li

In electron capture, an electron merges with a proton, forming a neutron. To identify the daughter nucleus, subtract one from the parent nucleus’ atomic number without changing its atomic mass. The element with an atomic number one less than beryllium is lithium.

Question 25

How do the products of positron emission differ from those of electron capture?

Answer 25

The products undergo identical changes. Specifically, each nucleus’ atomic number decreases by one, while its mass number is not changed.

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.

Question 26

What charge and mass do gamma rays have?

Answer 26

gamma rays have neither charge nor mass

A gamma ray is a high energy photon, a massless and uncharged particle.

Question 27

Define:

gamma decay

Answer 27

A form of radioactive decay in which a nucleus emits a gamma ray.

While the daughter nucleus of gamma emission will have lower energy, it will have identical atomic and mass numbers to the parent nucleus.

Question 28

A sample of radioactive nuclei has a mass of 10 g. After 590 years, only 5 g of the original nuclei remain. In this example, what term is given to the 590-year time period?

Answer 28

590 years is the half-life of this isotope, or the time it takes for exactly one-half of the original atoms to undergo radioactive decay.

After one half-life elapses, exactly half of the original number of parent nuclei will be present; the remainder will have decayed into daughter nuclei.

Question 29

Radioactive isotope X has a half-life of one hour. What proportion of the original amount of X will remain after 3 hours?

Answer 29

One-eighth of the original amount will remain.

For each half-life that elapses, one-half of the isotopes decay. After one hour, half of the original population remains. During the second hour, half of the remaining amount (an additional quarter of the starting amount) decays, leaving one quarter of the original population. In the third hour, half of the remaining quarter, or one-eighth of the starting amount, decays; this leaves one eighth of the original quantity.

Question 30

Radioactive isotope Z has a half-life of 3 days. How long will it take a 120-gram sample of Z to decay until only 30 grams remain?

Answer 30

6 days

For each half-life that elapses, one-half of the remaining isotopes will decay. After 3 days, 60 g of Z will have decayed, leaving 60 g. After 3 more days, an additional half of that 60 g will have decayed, leaving 30 g.

Question 31

Define:

nuclear fission

Answer 31

A radioactive process in which a nucleus splits into multiple lighter nuclei.

For example, an atom of ²³⁶U can be divided into an atom of ⁹²Kr, an atom of ¹⁴²Ba, and 2 free neutrons. Note that you do not need to memorize any specific fission reactions for the MCAT.

Question 32

Define:

nuclear fusion

Answer 32

A radioactive process in which two nuclei combine to form a heavier one.

For example, 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. This actually occurs in the sun. Note that you do not need to memorize any specific fusion reactions for the MCAT.

Question 33

When the exact mass of a nucleus is measured, it is found to be less than the total masses of its protons and neutrons. What term describes this effect?

Answer 33

This phenomenon is called mass defect. The individual protons and neutrons in an atom’s nucleus will have a larger mass than the overall observed mass of the nucleus.

Mass defect occurs because some mass must be converted to energy to hold the nucleus together. The nucleus will consequently weigh less than the protons and neutrons that comprise it.

Question 34

Define:

binding energy

Answer 34

The energy required to split a nucleus into its individual protons and neutrons.

The binding energy is exactly the same magnitude as the mass defect. In other words, the energy released when a nucleus is formed equals the energy needed to break it apart.

Question 35

What equation relates a nucleus’ mass defect and its binding energy?

Answer 35

E = mc²

Where:

E = binding energy of the nucleus
m = mass defect of the nucleus
c = speed of light, 3 x 10⁸ m/s

Since the value of c² is so large, a very small mass defect corresponds to a very large binding energy.

Question 36

The mass of two free protons and two free neutrons is about 4.032 AMU, but the mass of an alpha particle is about 4.002 AMU. What explains the discrepancy?

Answer 36

The remaining 0.030 AMU is the binding energy of the alpha particle.

Remember that 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.

Question 37

The binding energy of an alpha particle is 28.3 MeV. How much energy is needed to separate an alpha particle into its components?

Answer 37

28.3 MeV is required to break apart the alpha particle.

Remember that the binding energy is the mass converted to energy when the nucleus is formed. That same amount of energy is required to break the nucleus apart.

Question 38

What does the Bohr model of the hydrogen atom show?

Answer 38

It describes a hydrogen atom as a positively-charged nucleus orbited by a single electron.

The electron can only exist in fixed energy orbits, called orbitals.

The electron must gain or lose a specific amount of energy to travel between energy levels.

Question 39

How can the possible energies of an electron in a hydrogen atom be calculated, according to the Bohr model?

Answer 39

E_n = -13.6/n² eV

Here, n is the principal quantum number of the orbital containing the electron. Energy will be negative for all values of n. Note that you do not need to memorize this equation, but you should know what it can be used to calculate.

Question 40

How will energy vary as the value of n increases, according to the Bohr model?

Answer 40

• Energy increases as n increases. This relationship is shown by the equation:

E_n = -13.6/n² eV.

E_n is the energy of between the nucleus and the electron and will always be negative. Since n appears in the denominator, increasing its value causes E_n to become less negative or more positive.

Question 41

What equation gives the energy change experienced by an electron as it moves from an orbital with principal quantum number n_i to n_f, according to the Bohr model?

Answer 41

The energy difference is:

ΔE = -13.6(1/n_f²-1/n_i²) eV

While you do not need to memorize this formula, it may appear on the exam. The alternative would require applying the Bohr model energy formula to both orbitals, then subtracting the initial energy from the final energy.

Question 42

When an electron jumps from n=1 to n=2, by what amount does its energy increase?

Answer 42

Its energy increases by 10.2 eV.

Use the formula ΔE = -13.6(1/n_f²-1/n_i²) eV.

We know that n_f = 2 and n_i = 1, giving
ΔE = -13.6(1/2²-1/1²)
= -13.6(1/4 -1) = -13.6(-3/4) = 10.2 eV

Question 43

What information can be obtained from the emission spectrum of a hydrogen atom?

Answer 43

The set of frequencies of light that can be released by a hydrogen atom. These particular frequencies are uniquely characteristic of hydrogen.

Every element has a distinct emission spectrum; the presence of a certain element can be proven by observing its spectral lines.

Question 44

How does the Bohr model explain the placement of the lines in hydrogen’s emission spectrum?

Answer 44

Each spectral line is a result of the difference in energies between orbitals.

When an electron in a higher-energy orbital falls into a lower-energy state, 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 larger energy difference results in a higher photon frequency.