Atomic and Nuclear Physics - AP Physics 2
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What is the speed of an electron in the first Bohr orbit in meters per second?
What is the speed of an electron in the first Bohr orbit in meters per second?
To find the speed of the electron, use the following formula:
Substitute all the knowns and solve for velocity.
To find the speed of the electron, use the following formula:
Substitute all the knowns and solve for velocity.
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Suppose that an electron within a hydrogen atom moves from the fourth energy level to the second energy level. What is the wavelength of the photon emitted during this process?
Suppose that an electron within a hydrogen atom moves from the fourth energy level to the second energy level. What is the wavelength of the photon emitted during this process?
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.
To answer this question, we'll need to utilize the equation that specifies the energy level of electrons within a hydrogen atom.
Where
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.
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An electron collides with an atom, exciting an electron in the atom from it's ground state 
. The initial velocity of the incoming electron is 
and after the collision it has a velocity of 
. What is the energy of the excited electron in the atom after the collision in electron-volts?
An electron collides with an atom, exciting an electron in the atom from it's ground state
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
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
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 -
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Calculate the energy released as a photon when an electron falls from the 
energy level to the 
energy level.
Calculate the energy released as a photon when an electron falls from the
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.
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
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An electron in a hydrogen atom falls from the 
level to the 
level. What is the energy of the photon emitted?
An electron in a hydrogen atom falls from the
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
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
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How much energy would it take to raise an electron from the 
to the 
energy level of a hydrogen atom?
How much energy would it take to raise an electron from the
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 formula for the energy of an electron in a hydrogen atom's nth energy level:
Plug in
Convert electronvolts to Joules:
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One mole of hydrogen atoms have electrons drop from the 
energy level to the 
energy level. Determine the energy released.
One mole of hydrogen atoms have electrons drop from the
Using the following equation for the energy of an electron in Joules:
And
Combining equations and plugging in values:
would be released
Using the following equation for the energy of an electron in Joules:
And
Combining equations and plugging in values:
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What is the difference in energy for a hydrogen atom with its electron in the ground state and a hydrogen atom with its electron in the 
state?
What is the difference in energy for a hydrogen atom with its electron in the ground state and a hydrogen atom with its electron in the
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.
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,
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
Next, we can find the difference in the energy values.
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__________ is the process of combining two or more atoms into a single, larger atom. __________ is the process of splitting a single atom into two or more smaller atoms. __________ can occur in nature—in a star, for example. __________ doesn't normally occur in nature.
__________ is the process of combining two or more atoms into a single, larger atom. __________ is the process of splitting a single atom into two or more smaller atoms. __________ can occur in nature—in a star, for example. __________ doesn't normally occur in nature.
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.
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.
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Which of the fundamental forces is responsible for holding neutrons and protons together in the nucleus of an atom?
Which of the fundamental forces is responsible for holding neutrons and protons together in the nucleus of an atom?
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.
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.
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Suppose that an atom undergoes a series of decays. First, it undergoes two alpha decays, followed by two positron decays, and then finally by two gamma decays. How has the atomic number of this atom changed?
Suppose that an atom undergoes a series of decays. First, it undergoes two alpha decays, followed by two positron decays, and then finally by two gamma decays. How has the atomic number of this atom changed?
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.
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Compound X is found to radioactively decay with a rate constant equal to 
. If a time of 20min passes by, what percentage of Compound X has decayed within this period?
Compound X is found to radioactively decay with a rate constant equal to
To begin with, we'll have to make use of the radioactive decay equation:
Where:
= the amount of Compound X after an amount of time, 
, has passed
= the amount of Compound X at the start
= rate constant for the decay process
= the amount of time that has passed
Rearranging, we can see that:
Furthermore, we can convert minutes into seconds.
Next, we can plug the values we have into the above equation to obtain:
From the above expression, we see that:
This means that after a time of 20min has elapsed, there will be 
as much of Compound X as there was when at the beginning. Since there is 
remaining after this time period, then we can conclude that 
of Compound X has degraded within this amount of time.
To begin with, we'll have to make use of the radioactive decay equation:
Where:
Rearranging, we can see that:
Furthermore, we can convert minutes into seconds.
Next, we can plug the values we have into the above equation to obtain:
From the above expression, we see that:
This means that after a time of 20min has elapsed, there will be
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Which of the following types of decay particles is known as a positron?
Which of the following types of decay particles is known as a positron?
Positron decay (positive beta decay) is where a proton is converted into a neutron, a positron, and an electron neutrino.
Positrons are called 
particles (beta plus particles). They are the antiparticle to 
particles (the antimatter version of electrons). They are used in the medical field for PET (Positron Emission Tomography) scans by highlighting a radioactive substance (called a tracer) ingested earlier to show how organs and tissues are working. In nuclear reactors, they cause the water coolant to give a blue glow called Cherenkov radiation. This is because the positrons move faster than light does through water.
Positron decay (positive beta decay) is where a proton is converted into a neutron, a positron, and an electron neutrino.
Positrons are called
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The half-life of carbon-14 is 5730 years.
Rex the dog died in 1750. What percentage of his original carbon-14 remained in 1975 when he was found by scientists?
The half-life of carbon-14 is 5730 years.
Rex the dog died in 1750. What percentage of his original carbon-14 remained in 1975 when he was found by scientists?
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,
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You measure the beta decay activity of an unknown substance to be 
. 48 hours later, the activity is 
.
What is the half life in hours?
You measure the beta decay activity of an unknown substance to be
What is the half life in hours?
Use the following equation:
The decay constant is defined as:
From the first equation, we find:
Plug this value into the second equation above and solve.
Use the following equation:
The decay constant is defined as:
From the first equation, we find:
Plug this value into the second equation above and solve.
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A particular sample of a newly discovered isotope has an activity of 
. 10 minutes later, it has an activity of 
.
Determine the radioactive decay constant of this isotope.
A particular sample of a newly discovered isotope has an activity of
Determine the radioactive decay constant of this isotope.
Use the relationship:
Here, 
is the activity at a given time, 
is the initial activity, 
is the radioactive decay constant, and 
is the time passed since the initial reading.
Rearrange the equation to solve for 
.
Convert minutes to seconds and plug in values to solve for the radioactive decay constant.
Use the relationship:
Here,
Rearrange the equation to solve for
Convert minutes to seconds and plug in values to solve for the radioactive decay constant.
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A scientist tests a radioactive sample which has an activity of 
. 15 minutes later, it has an activity of 
.
Determine the number of radioactive nuclei in the initial sample.
A scientist tests a radioactive sample which has an activity of
Determine the number of radioactive nuclei in the initial sample.
Use the relationship:
Where 
is the activity at a given time, 
is the initial activity, 
is the radioactive decay constant and 
is the time passed since the initial reading.
Rearrange to solve for 
.
Convert minutes to seconds and plug in values to find the decay constant.
It is then necessary to use the relationship:
Where 
is the activity, 
is the decay constant and 
is the number of atoms.
Use the initial activity and the calculated decay constant to solve for the number of atoms:
Use the relationship:
Where
Rearrange to solve for
Convert minutes to seconds and plug in values to find the decay constant.
It is then necessary to use the relationship:
Where
Use the initial activity and the calculated decay constant to solve for the number of atoms:
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A scientist tests a radioactive sample which has an activity of . 15 minutes later, it has an activity of .
Determine the activity 18 minutes after the initial reading.
A scientist tests a radioactive sample which has an activity of
Determine the activity 18 minutes after the initial reading.
Use the relationship:
Where is the activity at a given time, is the initial activity, is the radioactive decay constant and is the time passed since the initial reading.
Rearrange to solve for
Convert minutes to seconds and plug in values.
Again use the relationship:
Use the new 
, which is equal to 
to plug in and solve for the activity.
Use the relationship:
Where
Rearrange to solve for
Convert minutes to seconds and plug in values.
Again use the relationship:
Use the new
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A scientist test a radioactive sample which has an activity of . 15 minutes later, it has an activity of .
Determine the half life of this isotope.
A scientist test a radioactive sample which has an activity of
Determine the half life of this isotope.
Use the relationship:
Here, is the activity at a given time, is the initial activity, is the radioactive decay constant, and is the time passed since the initial reading.
Rearrange the equation to solve for .
Convert minutes to seconds and plug in values.
Use the relationship:
Plug in the calculated value for 
:
Use the relationship:
Here,
Rearrange the equation to solve for
Convert minutes to seconds and plug in values.
Use the relationship:
Plug in the calculated value for
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A scientist test a radioactive sample which has an activity of . 15 minutes later, it has an activity of .
Determine the nuclear decay constant of this isotope.
A scientist test a radioactive sample which has an activity of
Determine the nuclear decay constant of this isotope.
Use the relationship:
Here, is the activity at a given time, is the initial activity, is the radioactive decay constant, and is the time passed since the initial reading.
Rearrange the equation to solve for .
Convert minutes to seconds and plug in values.
Use the relationship:
Here,
Rearrange the equation to solve for
Convert minutes to seconds and plug in values.
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