Atomic and Nuclear Physics - AP Physics 2

Fusion is the process of combining two or more atoms to form a larger atom. To remember this, think of how welders fuse metals together. (Though the term is the same, they aren't actually the same thing; this is just to help you remember.). Fusion is a very energetic reaction that takes place in high-heat, high-pressure environments, like the inside of stars. Fusion releases lots of energy, which is why stars are so energetic.

Fission is the process of splitting a signle atom into multiple atoms. It doesn't normally occur in nature, though some super heavy elements, like plutonium, can be spontaneously fissile, which means they can undergo fission seemingly at random. This is a rare thing for an element to do, which is why it's said that fission doesn't normally occur in nature.

The correct answer is quarks. Quarks usually have charges of or . They are usually bound with other quark particles and could be mixed to form hadrons. Tau is part of the leptons family and has a charge of . Graviton does not have a charge, and is a hypothetical particle. The tachyon is a hypothetical particle assumed to be faster than light. Hadrons are strong composite particles that are composed of quarks and will result to a net integer charge.

To answer this question, we'll need to consult the periodic table. From the table, we know that magnesium's atomic number (the number of protons it contains in its nucleus) is 12, and sodium's is 11. We also need to realize that the mass number for each (the number of protons plus neutrons contained in the nucleus) is the same. Since the mass numbers are the same but the atomic numbers differ by one, then we can infer that a neutron is undergoing a decay into a proton and a so called positron, . The overall reaction is as follows:

Furthermore, it cannot be alpha decay, because in this process an alpha nucleus is released and the reactant's mass number and atomic number would both change. It also cannot be gamma decay, because in this process there is no change in atomic or mass numbers. Finally, it cannot be electron capture because in this process, an electron combines with a proton to generate a neutron. Thus, the mass number would not change, but the atomic number would increase by one. But in the question stem, we know the atomic number is decreasing by one rather than increasing.

Neutrons and gluons both have no charge at all, so they can be ignored. The proton and the antiproton have the same mass but opposite charges, and so have the same ration of charge:mass. However, the electron has equal charge to both the proton and the antiproton, and has a ridiculously small mass comparatively. The mass of a proton/antiproton is , while the mass of an electron is , almost 2000 times as small as a proton. Therefore, the charge:mass ratio of the electron is the smallest of the fundamental particles listed.

To find the speed of the electron, use the following formula:

Substitute all the knowns and solve for velocity.

To answer this question, we'll need to utilize the equation that specifies the energy level of electrons within a hydrogen atom.

Where is equal to the electron energy level within the hydrogen atom. Also notice that this equation has a negative sign. This is because in its ground state, an electron is closest to the positively charged nucleus and thus has the lowest energy. As the energy level increases, the electron moves further and further away from the nucleus, thus gaining increasing energy. At an infinitely far away energy level, the electron will have a maximum energy value of zero. To find the difference between the second and fourth energy levels, we'll simply use the above equation for different values of .

The negative sign for the change in energy just means that energy is being released in this process. We can drop the negative because we know that energy is being released.

Now that we've found how much energy is contained in the released photon, we'll need to calculate its wavelength.

The incoming electron will lose kinetic energy during the collision, transfering this energy to the potential energy of the bound electron in the atom. Conservation of energy can be used to solve this problem. The general statement that energy is conserved is

where is the kinetic energy and is the potential energy. The incoming electron has kinetic energy and no potential energy. We are defining the initial state of the bound electron to be at so the total initial potential energy of the system is zero.

The incoming electron will still have kinetic energy after the collision but the bound electron will not since it is not a free electron. This means that

where

plugging this in -

is the mass of the electron. Plugging everything in and converting to gives

During a energy level change in a hydrogen atom, the amount of energy either lost of gained is given by the following equation with respect to the initial and final energy levels shown below.

Recall that whenever electrons drop from higher energy levels to lower ones, energy can be released in the form of a photon. To obtain the amount of energy released, we mst take the difference in energy of the electrons at the particular energy levels:

It is important to note that the negative energy difference corresponds to how much energy the photon is "taking away" as it leaves. Therefore, the photon leaves the atom with of energy.

Using

Plugging in values:

This will be the change in energy of the electron, which is the negative of the energy of the photon released.

Thus, the energy of the photon is

Using the formula for the energy of an electron in a hydrogen atom's nth energy level:

Plug in and then find the difference:

Convert electronvolts to Joules:

Using the following equation for the energy of an electron in Joules:

And

Combining equations and plugging in values:

would be released

For this question, we need to compare the difference in energy levels of hydrogen atoms with electrons in different orbitals.

First, we will need to use the equation that describes the energy of an electron in a hydrogen atom.

In the above expression, represents the orbital in which the electron resides.

First, let's see what the electron energy level is in the ground state, which corresponds to .

Next, let's do the same thing for the orbital.

Next, we can find the difference in the energy values.

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.

To find the speed of the electron, use the following formula:

Substitute all the knowns and solve for velocity.

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.

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.

To find the speed of the electron, use the following formula:

Substitute all the knowns and solve for velocity.

To answer this question, we'll need to utilize the equation that specifies the energy level of electrons within a hydrogen atom.

Where is equal to the electron energy level within the hydrogen atom. Also notice that this equation has a negative sign. This is because in its ground state, an electron is closest to the positively charged nucleus and thus has the lowest energy. As the energy level increases, the electron moves further and further away from the nucleus, thus gaining increasing energy. At an infinitely far away energy level, the electron will have a maximum energy value of zero. To find the difference between the second and fourth energy levels, we'll simply use the above equation for different values of .

The negative sign for the change in energy just means that energy is being released in this process. We can drop the negative because we know that energy is being released.

Now that we've found how much energy is contained in the released photon, we'll need to calculate its wavelength.

The incoming electron will lose kinetic energy during the collision, transfering this energy to the potential energy of the bound electron in the atom. Conservation of energy can be used to solve this problem. The general statement that energy is conserved is

where is the kinetic energy and is the potential energy. The incoming electron has kinetic energy and no potential energy. We are defining the initial state of the bound electron to be at so the total initial potential energy of the system is zero.

The incoming electron will still have kinetic energy after the collision but the bound electron will not since it is not a free electron. This means that

where

plugging this in -

is the mass of the electron. Plugging everything in and converting to gives

During a energy level change in a hydrogen atom, the amount of energy either lost of gained is given by the following equation with respect to the initial and final energy levels shown below.

Recall that whenever electrons drop from higher energy levels to lower ones, energy can be released in the form of a photon. To obtain the amount of energy released, we mst take the difference in energy of the electrons at the particular energy levels:

It is important to note that the negative energy difference corresponds to how much energy the photon is "taking away" as it leaves. Therefore, the photon leaves the atom with of energy.