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.

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.

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.

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.

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.

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.

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.

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 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: