Help with Radioactive Decay - AP Chemistry

This is the definition of gamma radiation.

Radioactive decay is the result of an unstable nucleus in an atom. When an atom contains more neutrons than the nucleus can handle it will undergo radioactive decay, leading to emission of different particles such as alpha particles or beta electrons. This can occur in ground state elemental atoms, but is most commonly seen in radioactive isotopes. Isotopes contain the same number of protons as any other atom of a given element, but often contain a greater number of neutrons, leading to instability. These neutrons will be lost via radioactive decay in order for the atom to reach the ground state, the most stable isotope.

Ionization results in a charged particle via electron transfer, but does not contribute to radioactivity.

Gamma radiation is the only form of radioactive decay that does not emit a physical particle from the atomic nucleus. It is simply the release of energy in the form of high energy gamma rays, which do not carry any mass. These rays are more powerful than any other electromagnetic wave known to man.

Alpha decay results in the release of a helium nucleus. Beta decay results in the release of an electron or a positron. Electron capture results in the emission of a neutron.

A half life is the amount of time it takes a radioactive sample to decay by 50%. To reach 25% of the initial dose would take two half lives.

It will take 220 minutes, or 3 hours and 40 minutes, for there to be 25% of the sample remaining. Since the sample was administered at 9am, this means that there will be less than 25% remaining at 1pm.

Alpha decay, beta decay, and positron emission are all commonly recognized forms of radioactive decay. Electron capture is another form of nuclear alteration via radioactivity. The nucleolus is a biological structure found in cells, and has no relation to the atomic nuclei described in chemistry.

During alpha decay, an element emits a helium nucleus with 2 neutrons and 2 protons. Thus, the atomic mass of the new element is decreased by four, and the atomic number is decreased by two.

Three subsequent alpha decays result in a new element with an atomic mass of 232 - 3(4) = 220, and a new atomic number of 90 - 3(2) = 84.

Using the periodic table, we find the element with this atomic number is polonium (Po).

In alpha decay, a helium nucleus is emitted, and thus the isotope loses 2 protons and 2 neutrons.

In electron emission, a neutron in the nucleus is converted into a proton and an emitted electron.

In positron emission, a proton in the nucleus is converted into a neutron and an emitted positron.

The given isotope will lose 4 protons and 4 neutrons via alpha emission, gain 1 proton and lose 1 neutron via electron emission, and lose 2 protons and gain 2 neutrons via positron emission. The result is a loss of 5 protons and 8 mass units.

Accounting for the changes in atomic mass and number, we find that the final element is 141-praseodymium.

By definition, half-life is the amount of time it takes for a radioactive substance to decrease by one-half its original value. In this question, the isotope's half life is 20min, meaning after 20min, 1g of the isotope will be reduced to 0.5g. After another 20min, 0.5g of the isotope will be reduced to 0.25g. Adding up the two 20min time frames it took to go from 1g of substance to 0.25g gives 40min.

There is an equation to calculate half-life problems, but if the sample is cut into halves every half-life, there is a simple way to find the time passed. Let's start with the total mass of the sample at time . For every the sample size will be cut in half:

After there will be of the isotope left.

For problems with half-life, we will use the equation

Where is the initial mass of the sample, is the amount left after time passes and is the half-life of the isotope. We have

To estimate the half-life we just see how long it takes for the sample to be cut in half. The green lines indicate when there is half the initial sample () which happens after passes. Therefore the half-life is .

Check: Will the sample be cut in half again after another ? The orange lines indicate the mass of the sample after another half-life and indeed there is now which is half of .

First of all, it's important to understand terminology used in this kind of a concept question. A nuclide refers to a particular atom or nucleus with neutrons and protons. As we know, neutrons refer to the neutrally charged particles within a nucleus, while protons refer to those that are positively charged.

The zone of stability is a roughly linear pattern that follows a positive correlation with number of protons and neutrons. As the number of protons increases in the nucleus, so does the number of neutrons to allow for stability.

When a nuclide falls above or below the zone of stability, it creates a beta or alpha positron, respectively. These nuclides would not be considered stable, as they show degradation over time.

This is the definition of gamma radiation.

Radioactive decay is the result of an unstable nucleus in an atom. When an atom contains more neutrons than the nucleus can handle it will undergo radioactive decay, leading to emission of different particles such as alpha particles or beta electrons. This can occur in ground state elemental atoms, but is most commonly seen in radioactive isotopes. Isotopes contain the same number of protons as any other atom of a given element, but often contain a greater number of neutrons, leading to instability. These neutrons will be lost via radioactive decay in order for the atom to reach the ground state, the most stable isotope.

Ionization results in a charged particle via electron transfer, but does not contribute to radioactivity.

Gamma radiation is the only form of radioactive decay that does not emit a physical particle from the atomic nucleus. It is simply the release of energy in the form of high energy gamma rays, which do not carry any mass. These rays are more powerful than any other electromagnetic wave known to man.

Alpha decay results in the release of a helium nucleus. Beta decay results in the release of an electron or a positron. Electron capture results in the emission of a neutron.

A half life is the amount of time it takes a radioactive sample to decay by 50%. To reach 25% of the initial dose would take two half lives.

It will take 220 minutes, or 3 hours and 40 minutes, for there to be 25% of the sample remaining. Since the sample was administered at 9am, this means that there will be less than 25% remaining at 1pm.

Alpha decay, beta decay, and positron emission are all commonly recognized forms of radioactive decay. Electron capture is another form of nuclear alteration via radioactivity. The nucleolus is a biological structure found in cells, and has no relation to the atomic nuclei described in chemistry.

During alpha decay, an element emits a helium nucleus with 2 neutrons and 2 protons. Thus, the atomic mass of the new element is decreased by four, and the atomic number is decreased by two.

Three subsequent alpha decays result in a new element with an atomic mass of 232 - 3(4) = 220, and a new atomic number of 90 - 3(2) = 84.

Using the periodic table, we find the element with this atomic number is polonium (Po).

In alpha decay, a helium nucleus is emitted, and thus the isotope loses 2 protons and 2 neutrons.

In electron emission, a neutron in the nucleus is converted into a proton and an emitted electron.

In positron emission, a proton in the nucleus is converted into a neutron and an emitted positron.

The given isotope will lose 4 protons and 4 neutrons via alpha emission, gain 1 proton and lose 1 neutron via electron emission, and lose 2 protons and gain 2 neutrons via positron emission. The result is a loss of 5 protons and 8 mass units.

Accounting for the changes in atomic mass and number, we find that the final element is 141-praseodymium.

By definition, half-life is the amount of time it takes for a radioactive substance to decrease by one-half its original value. In this question, the isotope's half life is 20min, meaning after 20min, 1g of the isotope will be reduced to 0.5g. After another 20min, 0.5g of the isotope will be reduced to 0.25g. Adding up the two 20min time frames it took to go from 1g of substance to 0.25g gives 40min.