MCAT Physical - Radioactive Decay

What is the product when $^{158}_{65}Tb$ undergoes an alpha decay?

$^{154}_{63}Eu$

$^{154}_{65}Tb$

$^{164}_{67}Ho$

$^{151}_{63}Eu$

Explanation

Alpha decay is the loss of a helium atom from the original particle.

$^{158}_{65}Tb \rightarrow ^{4}_{2}He + ^{154}_{63}Eu$

The number of protons is reduced by two, and the nuclear mass is reduced by four.

Which type of nuclear decay is displayed below?

$^{1}_1p \rightarrow ^{1}_0n + ^{0}_{+1}e$

Positron emission

Beta decay

Alpha decay

Electron capture

Gamma decay

Explanation

Positron emission is when the nucleus ejects a positron, or positive equivalent of an electron. It is also known as $\beta ^{+}$ decay.

Beta decay is when the nucleus ejects a beta particle (electron).

Alpha decay is when the nucleus ejects an alpha particle (helium nucleus).

Electron capture is when the nucleus caputres an electron from the inner most shell. This process converts a proton to a neutron.

Finally, gamma decay is when an excited nucleus emits gamma rays. Gamma rays have no mass or charge.

$_{6}^{14}\textrm{C} \rightarrow _{7}^{14}\textrm{N} + ?$

Which of the following best describes the missing component in the reaction above?

An electron

A neutron

An alpha particle

A photon

A hydrogen nucleus

Explanation

This is an example of beta decay because the atomic number increases (from 6 to 7). This means a neutron has decayed into a proton, which occurs by emitting an electron, $_{-1}^{0}\textrm{e}$ .

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.

Xe-135 has a half life of around 9.2 hours. A reaction generated 70g of Xe-135, as measured by a scientist on a Friday afternoon. If he returned 46 hours later to study the sample, how much would remain?

14g

70g

Explanation

The scientist allowed the substance to sit for a duration that was equal to five of its half life. The original sample decayed from 70g, to 35g, to 17.5g, to 8.75g, to 4.35g, to ~2 g.

$\frac{46\ hours}{9.2\ hours}=5$

$m_{remaining}=m_{original}(0.5)^n$

n is equal to the number of half lives that have passed. For us, n is equal to 5.

$m_{remaining}=(70g)(0.5)^5=(70g)(\frac{1}{32})=2.2g$

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

Alpha decay

Beta decay

Electron capture

Positron emission

All of these will alter the mass number

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.

The activity of a radioactive element is $\small 240 Bq$ . After $\small 24min$ , the activity is $\small 60Bq$ . What is the half-life of this element?

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:

$A_E=A_0(0.5)^{\frac{t}{t_{0.5}}}$

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.

$60Bq=(240Bq)(0.5)^{\frac{24}{x}}$

$0.25=(0.5)^{\frac{24}{x}}$

$2=\frac{24}{x}$

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

$_{92}^{238}U\rightarrow _{90}^{236}Th+2H$

$_{27}^{60}Co\rightarrow_{27}^{60}Co+\gamma$

$_6^{14}C\rightarrow\ _7^{14}N+\ _{-1}^0e$

$_{92}^{238}U\rightarrow _{90}^{234}Th+_2^4He$

$_{6}^{14}\textrm{C}\rightarrow\ _{5}^{14}\textrm{B}+\ _{1}^{0}\textrm{e}$

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 $_{92}^{238}U\rightarrow _{90}^{236}Th+2H$ . No such decay process emitting hydrogen atoms exists.

Nuclear reactions, such as the one described above with uranium, emit energy in the form of radiation. A scientist is considering three different forms of radiation to generate power. Which of the following types of radiation is highest in energy?

Gamma radiation

Alpha radiation

Beta radiation

Positron emission

Electron capture

Explanation

Gamma radiation is a highly energetic form of radiation, and is the type of radiation emitted when antimatter and matter annhilate each other upon contact.

The half-life of a particular isotope of radium is 1600 years. If a sample of this isotope originally has a mass of 120g, how long would it take the mass of this isotope to decrease to 15g?

4800 years

6400 years

3200 years

1600 years

800 years

Explanation

First note that 15g is 1/8 of the original 120-gram mass, so all but 1/8 of these radium nuclei have decayed. By definition, ½ of the nuclei decay during one half-life. So the number of nuclei remaining after n half-lives is $\small (\frac{1}{2})^{n}$ . In this case, three half-lives have elapsed since, $\small \frac{1}{8} = (\frac{1}{2})^{3}$ . The answer is 3 * 1600 = 4800 years.

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