Quantum 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.

This is an example of one of Einstein's greatest ideas: the relation between the mass of an object/particle, and the energy contained by the mass. This is given as

In order to calculate the energy in our particle, we must make sure that the mass is in units of .

Now we can plug in numbers to our equation and solve for energy.

In this question, we're presented with information concerning the mass of a uranium atom. We're told two values: the mass of a uranium atom as measured, and the predicted mass of a uranium atom. We're then asked to determine the nuclear binding energy for uranium.

In order to solve this question, we have to realize the significance of the discrepancy between the observed and predicted mass of uranium. The predicted mass is calculated by adding up the individual masses of each constituent proton, electron, and neutron. However, the reason why the measured mass is less than the predicted mass is due to energy-mass equivalence. When the constituent protons and neutrons come together to form the nucleus, some of their mass is converted into energy, and it is this energy which holds these constituent nucleons together. Because some of the mass is converted into energy, the observed mass is less than what we would predict.

Now that we understand why there is a discrepancy between observed and predicted mass, we can calculate the nuclear binding energy by using Einstein's famous equation.

This equation states that the nuclear binding energy is equal to the difference between observed and predicted mass, multiplied by the speed of light squared. So to solve for energy, we can plug in the values given to us.

The energy from the two grams of helium can be found using

This energy can then be equated to the man's kinetic energy, which can then be used to find the man's velocity.

In this question, we're given the mass defect of an atom's nucleus and are asked to find the binding energy for this atom.

To begin with, it's important to understand that when protons and neutrons come to be held together within the nucleus of an atom, there is a tremendously powerful force holding them together. This incredibly large force accounts for the mass defect. In other words, the total mass of the nucleus is smaller than the sum of the individual masses of the protons and neutrons that make up that nucleus, and this is due to the strong force.

Einstein's mass-energy equivalence explains the observable mass defect; the mass lost is converted into an enormous amount of energy according to the following equation.

But first, we'll need to convert the mass given to us in the question stem into grams.

Furthermore, because we know the value for the speed of light, we can use this information to solve for the binding energy.

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.

This is an example of one of Einstein's greatest ideas: the relation between the mass of an object/particle, and the energy contained by the mass. This is given as

In order to calculate the energy in our particle, we must make sure that the mass is in units of .

Now we can plug in numbers to our equation and solve for energy.

In this question, we're presented with information concerning the mass of a uranium atom. We're told two values: the mass of a uranium atom as measured, and the predicted mass of a uranium atom. We're then asked to determine the nuclear binding energy for uranium.

In order to solve this question, we have to realize the significance of the discrepancy between the observed and predicted mass of uranium. The predicted mass is calculated by adding up the individual masses of each constituent proton, electron, and neutron. However, the reason why the measured mass is less than the predicted mass is due to energy-mass equivalence. When the constituent protons and neutrons come together to form the nucleus, some of their mass is converted into energy, and it is this energy which holds these constituent nucleons together. Because some of the mass is converted into energy, the observed mass is less than what we would predict.

Now that we understand why there is a discrepancy between observed and predicted mass, we can calculate the nuclear binding energy by using Einstein's famous equation.

This equation states that the nuclear binding energy is equal to the difference between observed and predicted mass, multiplied by the speed of light squared. So to solve for energy, we can plug in the values given to us.

The energy from the two grams of helium can be found using

This energy can then be equated to the man's kinetic energy, which can then be used to find the man's velocity.

In this question, we're given the mass defect of an atom's nucleus and are asked to find the binding energy for this atom.

To begin with, it's important to understand that when protons and neutrons come to be held together within the nucleus of an atom, there is a tremendously powerful force holding them together. This incredibly large force accounts for the mass defect. In other words, the total mass of the nucleus is smaller than the sum of the individual masses of the protons and neutrons that make up that nucleus, and this is due to the strong force.

Einstein's mass-energy equivalence explains the observable mass defect; the mass lost is converted into an enormous amount of energy according to the following equation.

But first, we'll need to convert the mass given to us in the question stem into grams.

Furthermore, because we know the value for the speed of light, we can use this information to solve for the binding energy.

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.