To find the approximate age of the sample, we need to consider the half-life of the starting material, substance A. We also need to consider the relative amounts of substance A and substance B.

Since we are told that the sample we are looking at contains substance A and substance B, we know that the sample must have started out with of substance A. Furthermore, in order to go from to , we know that a total of two half-lives must have passed. And since we know that one half-life is equal to , we can conclude that a total of must have passed.

225 years have passed since Rex died. Find the number of half-lives that have elapsed.

To find the proportion of a substance that remains after a certain number of half-lives, use the following equation:

Here, is the number of half lives that have elapsed.

225 years have passed since Rex died. Find the number of half-lives that have elapsed.

To find the proportion of a substance that remains after a certain number of half-lives, use the following equation:

Here, is the number of half lives that have elapsed.

To find the approximate age of the sample, we need to consider the half-life of the starting material, substance A. We also need to consider the relative amounts of substance A and substance B.

Since we are told that the sample we are looking at contains substance A and substance B, we know that the sample must have started out with of substance A. Furthermore, in order to go from to , we know that a total of two half-lives must have passed. And since we know that one half-life is equal to , we can conclude that a total of must have passed.

Using the relationship:

Here, is the activity at a given time, is the intial activity, is the radioactive decay constant, and is the time passed since the initial reading.

Rearranging the equation to solve for .

Converting minutes to seconds and plugging in values.

Again using the relationship

Using the new

Using the relationship:

Here, is the activity at a given time, is the intial activity, is the radioactive decay constant, and is the time passed since the initial reading.

Rearranging the equation to solve for .

Converting minutes to seconds and plugging in values.

Again using the relationship

Using the new

In this question, we're told that an atom undergoes a series of decays. We're then asked to determine how the atomic number of that atom has changed.

Let's look at the first type of decay, alpha decay. During alpha decay, the atom emits a helium nucleus, which consists of two protons and two neutrons. Thus, for each alpha decay, the atom will lose two protons. So two alpha decays would result in a net loss of four protons.

Next, let's look at positron decay. In this type of decay, a proton is converted into a positron and a neutron. The neutron stays in the atoms's nucleus, while the positron is emitted. Thus, positron decay results in a loss of one proton. Consequently, two positron decays result in a total loss of two protons.

Finally, gamma decay does not cause a change in the atom's atomic number or mass number. Gamma decay simply releases energy.

So, in total, we have four protons lost from alpha decays and two protons lost from positron decays. Thus, there is a total loss of six protons, corresponding to a decrease in the atomic number by six.

In this question, we're told that an atom undergoes a series of decays. We're then asked to determine how the atomic number of that atom has changed.

Let's look at the first type of decay, alpha decay. During alpha decay, the atom emits a helium nucleus, which consists of two protons and two neutrons. Thus, for each alpha decay, the atom will lose two protons. So two alpha decays would result in a net loss of four protons.

Next, let's look at positron decay. In this type of decay, a proton is converted into a positron and a neutron. The neutron stays in the atoms's nucleus, while the positron is emitted. Thus, positron decay results in a loss of one proton. Consequently, two positron decays result in a total loss of two protons.

Finally, gamma decay does not cause a change in the atom's atomic number or mass number. Gamma decay simply releases energy.

So, in total, we have four protons lost from alpha decays and two protons lost from positron decays. Thus, there is a total loss of six protons, corresponding to a decrease in the atomic number by six.

Using the relationship:

Here, is the activity at a given time, is the intial activity, is the radioactive decay constant, and is the time passed since the initial reading.

Rearranging the equation to solve for .

Converting minutes to seconds and plugging in values.

Using the relationship

Plugging in the calculated value for

First of all, the intermediate nuclear force isn't a real force.

Gravity is not responsible for this, because on the scale of quantum mechanical phenomena, gravity has negligible effect, and can be disregarded.

The electromagnetic force doesn't hold the nucleus together, and is actually trying to rip it apart, due to the fact that like charges repel and the nucleus is full of like charges (protons). Accordingly, the force that actually is responsible for holding it together must necessarily be significantly more powerful compared to the electromagnetic force to resist the intrinsic repelling the protons have towards each other.

The weak nuclear force operates on leptons and quarks, and is involved in many of the radioactive decays in nuclear physics, such as beta decay, where a proton decays into a neutron, where it was first revealed.

Since the other three valid forces aren't responsible, that leaves the strong nuclear force. It is the strongest of the four fundamental forces, as it prevents protons from flying away from each other due to their proximity and charge. The strong force mediates over the quarks that make up the protons and neutrons.