MCAT Physical : Radioactive Decay

Study concepts, example questions & explanations for MCAT Physical

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Example Question #21 : Nuclear Chemistry And Electrons

In the operation of nuclear reactors, engineers make use of substances known as neutron poisons. These are used to help store nuclear waste and slow nuclear reactions, but are also generated naturally in nuclear chain reactions as a by-product. This natural by-product can stop the desirable chain reaction present in a nuclear reactor used for power generation. 

For example, in nuclear power plants, U-235 is used as a fuel. U-235 absorbs a neutron, and subsequently generates neutrons (which power the chain reaction) and Xe-135. Xe-135 is a well-known neutron poison, and thus can impact the continued chain reaction of a nuclear power plant if it becomes over abundant during power generation. 

To help account for this, engineers have developed measurements to quantify the impact of Xe-135 on nuclear operations. For instance, the time during which there is an inability to start a reactor due to the buildup of Xe-135 is referred to as the precluded start-up time. Also, the amount of time that the reactor cannot override the effects of built up Xe-135 is called poison outage time. Perhaps the most important measure that engineers have developed is the neutron absorption capacity (σ), which is measured in units of barns and is a function of microscopic cross section. Xe-135 has a neutron absorption capacity of 2.00 * 106 barns, while another common poison, Sm-149, has a neutron absorption capacity of 74,500 barns.

When a U-235 atom breaks down __________.

Possible Answers:

the reaction absorbs an amount of energy, and then a greater amount is released when the new species form

the reaction absorbs an amount of energy, and then a lesser amount is released when the new species form

The reaction absorbs an amount of energy, and then an equal amount is released when the new species form

the reaction releases energy with no absorption

the reaction absorbs energy with no release

Correct answer:

the reaction absorbs an amount of energy, and then a greater amount is released when the new species form

Explanation:

Like any system, energy is absorbed to break bonds and released when bonds are formed. Energy is absorbed to get U-235 to an unstable state. It then breaks apart, and new species form. These new species release more energy than was originally absorbed when they form their bonds, thus leading to a net release of energy from the system.

Example Question #11 : Radioactive Decay

An isotope of uranium initially contains 92 protons and 146 neutrons. This isotope then undergoes two alpha decays, one beta () particle decay, and two gamma decays. How many neutrons does the resulting nucleus contain?

Possible Answers:

Correct answer:

Explanation:

To solve this question, you must be familiar with each type of radioactive decay.

Alpha decay emits two protons and two neutrons: .

Beta particle decay emits an electron, which has been converted from a neutron: .

Gamma decay is purely electromagnetic, with no attached particles: .

We start with uranium: .

The number of neutrons will be equal to the total mass number, minus the number of protons.

There will be 141 neutrons in the final product nucleus.

Example Question #11 : Radioactive Decay

What is the decay constant of krypton-96, if half of a sample decays to rubidium-96 in ?

Possible Answers:

Correct answer:

Explanation:

The general equation for exponential decay is:

represents the initial amount of the compound, is the decay constant, and is the time.

If half of the initial amount of krypton has decayed after , we can set up the equation as a proportion:

To get the variable out from the exponent, take the natural log of both sides.

Example Question #811 : Mcat Physical Sciences

The activity of a radioactive element is . After , the activity is . What is the half-life of this element?

Possible Answers:

Correct answer:

Explanation:

Radioactive elements spontaneously release particles. The half life is determined by the amount of time it takes half of a sample to release particles, thereby decreasing in mass and radioactive activity.

The formula for radioactive decay is:

We can solve for the half life by using the formula. We are given the initial and final activity values and the time period. Use these to solve for the half life.

Example Question #11 : Radioactive Decay

What is the daughter particle produced from -decay, followed by a single round of -decay, of ?

Possible Answers:

Correct answer:

Explanation:

Start with the parent particle, . Alpha decay will result in the loss of a helium nucleus: two protons and two neutrons.

Remember that a change in proton number must be associated with a change in elemental identity, changing gadolinium to samarium.

Next, the particle will undergo beta-decay. In this process, a neutron is converted to a proton and an electron. The result is no net change in mass, but an increase in proton number and the release of an electron.

The final result is a europium atom.

Example Question #813 : Mcat Physical Sciences

In the operation of nuclear reactors, engineers make use of substances known as neutron poisons. These are used to help store nuclear waste and slow nuclear reactions, but are also generated naturally in nuclear chain reactions as a by-product. This natural by-product can stop the desirable chain reaction present in a nuclear reactor used for power generation. 

For example, in nuclear power plants, U-235 is used as a fuel. U-235 absorbs a neutron, and subsequently generates neutrons (which power the chain reaction) and Xe-135. Xe-135 is a well-known neutron poison, and thus can impact the continued chain reaction of a nuclear power plant if it becomes over abundant during power generation. 

To help account for this, engineers have developed measurements to quantify the impact of Xe-135 on nuclear operations. For instance, the time during which there is an inability to start a reactor due to the buildup of Xe-135 is referred to as the precluded start-up time. Also, the amount of time that the reactor cannot override the effects of built up Xe-135 is called poison outage time. Perhaps the most important measure that engineers have developed is the neutron absorption capacity (σ), which is measured in units of barns and is a function of microscopic cross section. Xe-135 has a neutron absorption capacity of 2.00 * 106 barns, while another common poison, Sm-149, has a neutron absorption capacity of 74,500 barns.

A scientist is studying a nuclear reaction similar to the one in the passage. He finds that the atomic mass of the reactant does not change, but its atomic number decreases by one. This type of nuclear reaction is best described as __________.

Possible Answers:

Beta decay

Positron emission

Gamma decay

Alpha decay

Electron capture

Correct answer:

Positron emission

Explanation:

If the atomic number decreases by one, but the atomic mass is unchanged, the reactant must be converting one proton to a neutron. The resulting byproduct is a positron.

Notice that the positron on the right is released upon the rectant's conversion. This type of emission is known as positron emission.

Example Question #811 : Mcat Physical Sciences

Which of the following choices incorrectly represents a radioactive decay process?

Possible Answers:

Correct answer:

Explanation:

In general, there are three types of radioactive decay.

Alpha decay: An atomic nucleus emits a helium nucleus, composed of two protons and two neutrons. The net result is mass reduction of four (from the two neutrons and two protons) and an atomic number reduction of two (from the loss of two protons).

Beta decay: An atomic nucleus emits an electron, while a neutron splits into a proton, an electron, and anti-electron neutrino. The net result is an increase in atomic number (due to the added proton). Note, the atomic mass remains constant because although a neutron is lost, a proton is formed.

Possitron emmision: An atomic nucleus emits an anti-electron neutrino and electron, after a proton splits into a neutron. The net result is an decrease in atomic number (due to the tranformed proton). Note, the atomic mass remains constant because although a proton is lost, a neutron is formed.

Gamma Decay: The energy level of atomic nucleus drops, without losing protons or neutrons.

Each one of these decay processes are reflected individually in the answer choices, other than the decay process of . No such decay process emitting hydrogen atoms exists.

Example Question #12 : Radioactive Decay

Which of the following types of radioactive decay alters the mass number?

Possible Answers:

All of these will alter the mass number

Electron capture

Alpha decay

Beta decay

Positron emission

Correct answer:

Alpha decay

Explanation:

The mass number is the total number of nucleons (protons and neutrons) in an atom's nucleus. An atom that undergoes alpha decay will lose a helium nucleus. This decreases its mass number by four. All other forms of radioactive decay listed alter the atomic number of the atom, but not the mass number.

Beta emission involves the conversion of a neutron to a proton and an electron, but only expels the electron.

Electron capture involves the conversion of a proton and an electron into a neutron.

Positron emission involves the conversion of a proton to a neutron and a "positron," or positively charged electron.

Example Question #17 : Radioactive Decay

A sample of radioactive material decays from 64 atoms to 4 atoms in 6 hours. What is the half-life of this substance?

Possible Answers:

Correct answer:

Explanation:

The half-life is the time it takes to reduce a sample by one-half of the original quantity. The substance would have to go through four half-life cycles to go from 64 atoms to 4 atoms.

If the total time for four cycles is 6 hours, then the half life is:

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