Fiveable
Fiveable

or

Log in

Find what you need to study


Light

Find what you need to study

1.6 Photoelectron Spectroscopy

8 min readdecember 20, 2022

Jeremy Kiggundu

Jeremy Kiggundu

Dalia Savy

Dalia Savy

Jeremy Kiggundu

Jeremy Kiggundu

Dalia Savy

Dalia Savy

Understanding the structure of an atom is essential to comprehending the and interpreting photoelectron spectroscopy. Remember that an atom is made up of three subatomic particles:

  1. - located in the with a +1 charge and a mass of approximately 1 amu.

  2. - located in the with no charge and a mass of approximately 1 amu.

  3. - found around the in orbitals with a charge of -1 and no mass.

The movement of will be our focus in this study guide. Be sure to review how to write out the electron configuration of an atom and understand that are not only found in different energy levels or shells but are also located in different :

  • When writing out , the number (1, 2, 3, etc) represents the or electron shell.

  • Following the electron shell, you will letters (s, p, d, and f). These letters represent the four unique where can be located. The maximum number of in each subshell, respectively, is 2, 6, 10, and 14.

The following is the of , element 5 on the periodic table:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-CsN4D7KRdkFg.png?alt=media&token=89b3d198-c4af-4284-9e0d-bcd8e99769dc

👉 If you would like to review how this electron configuration was obtained, check out our study guide on "Atomic Structure and Electron Configuration."

The Quantum-Mechanical Model

Before this section, we have been discussing the atom with regard to Bohr's model. However, today chemists use the of an atom to more accurately display how behave. Rather than precisely defining where may exist around a , the displays how have the probability of existing almost anywhere.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-uDwek507VdQD.jpg?alt=media&token=123d1e65-4676-45e4-bd62-564398915382

Image Courtesy of dreamstime

Although you don't have to know this for the AP exam, it may help your understanding of this section. The biggest takeaway of the is , which basically states that it is virtually impossible to know both the exact position and momentum of a particle at the same time.

👉 For more information about this topic (if you're interested), check out this site.

The Properties of Light

Before we continue our exploration of , we have to understand the . Light has many properties in common with , such as its . and light exist as both a particle and a wave simultaneously. An electron's wave-like properties are basically the reason for .

Light as Particle

Let's focus on light as a particle, otherwise known as a ! proposed that light is made up of photons, each of which has a specific energy.

Frequency of Light

Frequency (v) represents the number of waves that pass a point in space in one second. You can think about the as the number of times a slinky goes back and forth in a second.

The is also related to its energy in a direct relationship. Light with a higher frequency has more energy than light with a lower frequency.

The Photoelectric Effect

The demonstrates that when a of sufficient energy hits a metal surface, it can emit an electron. In other words, are emitted from a metal surface when light strikes it if its frequency is high enough. ✨

Basically, the only occurs if the reaches a certain threshold:

  • If the frequency is low, the metal absorbs the light. It is not high enough to reach the threshold and therefore does not exhibit the .

  • If the frequency is high enough and reaches the threshold, a specified number of are ejected from the metal.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-xMfP7vOzibGj.gif?alt=media&token=728bdc25-82a2-4000-af5b-49e5c7a7d1d8

Image Courtesy of Google; you can see here that only photons that reach the given threshold of -2.0 eV can eject an electron from this metal, potassium.

We'll go over this concept in greater depth in unit three of the AP Chemistry curriculum.

Photoelectron Spectroscopy (PES)

Photoelectron spectroscopy (PES) is a technique used to compare the relative energies of atoms, ions, and molecules. PES uses energy from emitted through the to provide insight into the electronic configuration of a sample.

How does PES work?

When light of a certain frequency shines upon a sample, a limited number of are emitted. The released energy reflects the energy or energy levels within an atom. 

In viewing the photoelectron spectrum of an element, you are also able to:

  • Distinguish the different in an atom

  • Determine the of an atom.

Each peak in a photoelectron spectrum represents a different orbital level where can be found.

Here is a diagram putting all of these concepts together, but don't worry, we'll break it down further! 🎉

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-IhReCZoQ1akR.png?alt=media&token=05ad2e04-e165-4ed5-9598-7b75205075e3

Image Courtesy of Chemdx

Interpreting a Photoelectron Spectrum

Here is a photoelectron spectrum of without the markups which is how the AP exam would give you a graph like this. Let's dissect it.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-OmBxHLTMFO1l.png?alt=media&token=613bfdd9-2656-4ee1-b0ec-724e0d844605

Image Courtesy of Chemmybear

The Axes of a PES

First, let's look at the axes. When looking at a graph for the first time, the first thing you want to look at is what the graph is representing.

The x-axis is the , which is used very similarly to the term "" on the AP Chemistry exam. We'll go over ionization energy in the next study guide, but for now, think of it as the amount of energy required to remove an electron from an atom.

The closer an electron is to the of an atom, the more energy will be required to remove it. Therefore, the , or , will be higher as well. Think about this with regard to the fact that positive charges attract negative charges. The super-positive is going to be strongly attracted to the negative around it. that are closer to the are thus more strongly attracted to it.

This information should be able to tell us which side the is on in this diagram. With this photoelectron spectrum of , it is on the left side because the is greatest there (1000>0.1). So let's read the diagram from left to right.

The y-axis of this graph simply tells you how many there are in each peak.

The Peaks on a PES

Since peaks represent an orbital where can be found, the first orbital (closest to the ) must be 1s. Because the graph goes up to 2 on the y-axis, there are 2 in the . This should make sense because there is a maximum of two in the s suborbital.

The next orbital has to be 2s and the PES indicates there are 2 in this orbital as well.

So far, the seems to be 1s^2 2s^2.

There is one more peak though, which corresponds to the . However, this orbital isn't filled to maximum capacity, there are only 2 in it.

The full of this element is 1s^2 2s^2 2p^2. If I didn't tell you that this PES was for , you should be able to guess it given the graph and the periodic table.

Big Ideas with Photoelectron Spectroscopy

When breaking down a PES,

  • The position of the peak indicates how much energy is required to remove an electron from that sublevel.

  • The height of the peak indicates how many occupy that sublevel.

Practice MCQs

The next two questions are adapted from a Quizizz that kkehesci created.

  1. Refer to the photoelectron spectrum of neon shown below to answer the following question. Which of the following statements best accounts for peak A being to the left of peaks B and C?

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-7vN4jkEwOIVy.JPG?alt=media&token=92a83d1a-d86b-49fc-b3b3-7125f7f28d99

a. The of neon is 1s^2 2s^2 2p^6.

b. Neon has 8 located in its valence shell.

c. Core of an atom experience a much greater attraction to the than valence .

d. Peaks B and C show 1st ionization energies (I.E.) in neon, whereas peak A shows the 2nd I.E. of Neon.

2. Which peak shows closest to the ? A, B, C, or D?

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-gQTFZBKdv3Rh.JPG?alt=media&token=22a355f8-f21d-4eb5-9e69-da4bccea0f94

Answers to MCQs

  • The answer to #1 is C: core of an atom experience a much greater attraction to the than valence . This goes back to the concept that closest to the have a higher /.

  • The answer to #2 is peak A. This goes back to that same exact concept. If asked about which peak corresponds to the energies of the valence , you should say peak D (since they are furthest from the ).

AP Practice Question - 2019 #5

This question is taken from the AP Chemistry Exam in 2019.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-vYbo9p2LSU6V.JPG?alt=media&token=faaeb9e3-4535-424f-b262-c48f8790bc0b

In part a, they are asking you to simply write the and identify the element. We just did this a few times! If you feel comfortable with this, try it on your own first before looking at the answer.

Since the is the largest on the left, the peak on the left is the . The is:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-c9Hr7nMToV5W.JPG?alt=media&token=a4347fc2-4fc7-4403-a568-4f0a5fb3805d

You could use the noble gas shortcut here as well, but I often leave the like this when given a PES. You may make a mistake when trying to write out the noble gas shortcut with a photoelectron spectrum.

To identify the element, just pull out your periodic table! You should get Ca.

🎥 Watch Jacob Jeffries explain the parts of the atom and the experiments scientists use to study them.

Key Terms to Review (24)

1s Orbital

: The 1s orbital is closest orbital to nucleus in an atom. It can hold up to two electrons and has spherical shape.

2p Orbital

: The 2p orbital refers to the three atomic orbitals found on the second energy level (n=2), each with two lobes pointing in different directions along x,y,z axes respectively.

2s Orbital

: The 2s orbital is a type of atomic orbital, or region where an electron can exist within an atom. It's part of the second energy level (n=2) and has a spherical shape.

Albert Einstein

: Albert Einstein was a theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics. His work is also known for its influence on the philosophy of science.

Binding Energy

: Binding energy is the energy required to disassemble a whole system into separate parts. In chemistry, it often refers to the energy needed to remove an electron from an atom.

Boron

: Boron is a chemical element with the symbol B and atomic number 5. It's a metalloid, which means it has properties of both metals and non-metals.

Carbon

: Carbon is a chemical element with symbol C and atomic number 6. It's nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds.

Electron Configuration

: Electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure.

Electrons

: Electrons are subatomic particles with a negative electric charge. They orbit around the nucleus of an atom in specific energy levels or shells.

Frequency Of Light

: The frequency of light refers to the number of wave cycles that pass a given point per unit time. It determines color in visible light; high-frequency appears violet while low-frequency appears red.

Heisenberg's Uncertainty Principle

: Heisenberg's Uncertainty Principle states that it is impossible to simultaneously measure the exact position and momentum (velocity times mass) of a particle with absolute certainty.

Ionization Energy

: Ionization energy is the amount of energy required to remove an electron from a gaseous atom or ion.

Neutrons

: Neutrons are subatomic particles found in the nucleus of an atom. They have no electric charge and a mass slightly larger than that of a proton.

Nucleus

: The nucleus is at the center of an atom consisting mainly of protons and neutrons. It carries most of an atom's mass but occupies only a tiny space compared to the total size of the atom.

Orbital Levels

: Orbital levels refer to regions around an atom's nucleus where electrons are most likely found. They're often referred to as "energy levels" because each level corresponds with specific amounts of energy.

Photoelectric Effect

: The photoelectric effect refers to when electrons are ejected from matter after absorbing photons (light particles).

Photoelectron Spectroscopy (PES)

: Photoelectron Spectroscopy (PES) is a technique used to determine the energy levels of electrons in atoms or molecules. It involves shining light onto a sample and measuring the kinetic energy of the ejected electrons.

Photon

: A photon is a particle of light defined as a discrete bundle (or quantum) of electromagnetic (or light) energy. Photons are always in motion and, in vacuum, travel at a constant speed to all observers.

Principle Energy Level

: The principle energy level of an atom refers to the major energy levels, or shells, where electrons reside. These are denoted by the numbers 1, 2, 3 and so on.

Properties of Light

: The properties of light refer to the characteristics and behaviors that light exhibits, including reflection, refraction, interference, diffraction, polarization, and photoelectric effect.

Protons

: Protons are positively charged subatomic particles found within atomic nuclei.

Quantum-Mechanical Model

: The quantum mechanical model is based on quantum theory, which says matter also has properties associated with waves. It describes electrons as they move around the nucleus within regions called electron clouds or orbitals.

Subshells

: Subshells are a division of electron shells separated by different quantum numbers. They are designated as s, p, d, and f.

Wave-Particle Duality

: Wave-particle duality is the concept that all particles exhibit both wave-like and particle-like properties.

1.6 Photoelectron Spectroscopy

8 min readdecember 20, 2022

Jeremy Kiggundu

Jeremy Kiggundu

Dalia Savy

Dalia Savy

Jeremy Kiggundu

Jeremy Kiggundu

Dalia Savy

Dalia Savy

Understanding the structure of an atom is essential to comprehending the and interpreting photoelectron spectroscopy. Remember that an atom is made up of three subatomic particles:

  1. - located in the with a +1 charge and a mass of approximately 1 amu.

  2. - located in the with no charge and a mass of approximately 1 amu.

  3. - found around the in orbitals with a charge of -1 and no mass.

The movement of will be our focus in this study guide. Be sure to review how to write out the electron configuration of an atom and understand that are not only found in different energy levels or shells but are also located in different :

  • When writing out , the number (1, 2, 3, etc) represents the or electron shell.

  • Following the electron shell, you will letters (s, p, d, and f). These letters represent the four unique where can be located. The maximum number of in each subshell, respectively, is 2, 6, 10, and 14.

The following is the of , element 5 on the periodic table:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-CsN4D7KRdkFg.png?alt=media&token=89b3d198-c4af-4284-9e0d-bcd8e99769dc

👉 If you would like to review how this electron configuration was obtained, check out our study guide on "Atomic Structure and Electron Configuration."

The Quantum-Mechanical Model

Before this section, we have been discussing the atom with regard to Bohr's model. However, today chemists use the of an atom to more accurately display how behave. Rather than precisely defining where may exist around a , the displays how have the probability of existing almost anywhere.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-uDwek507VdQD.jpg?alt=media&token=123d1e65-4676-45e4-bd62-564398915382

Image Courtesy of dreamstime

Although you don't have to know this for the AP exam, it may help your understanding of this section. The biggest takeaway of the is , which basically states that it is virtually impossible to know both the exact position and momentum of a particle at the same time.

👉 For more information about this topic (if you're interested), check out this site.

The Properties of Light

Before we continue our exploration of , we have to understand the . Light has many properties in common with , such as its . and light exist as both a particle and a wave simultaneously. An electron's wave-like properties are basically the reason for .

Light as Particle

Let's focus on light as a particle, otherwise known as a ! proposed that light is made up of photons, each of which has a specific energy.

Frequency of Light

Frequency (v) represents the number of waves that pass a point in space in one second. You can think about the as the number of times a slinky goes back and forth in a second.

The is also related to its energy in a direct relationship. Light with a higher frequency has more energy than light with a lower frequency.

The Photoelectric Effect

The demonstrates that when a of sufficient energy hits a metal surface, it can emit an electron. In other words, are emitted from a metal surface when light strikes it if its frequency is high enough. ✨

Basically, the only occurs if the reaches a certain threshold:

  • If the frequency is low, the metal absorbs the light. It is not high enough to reach the threshold and therefore does not exhibit the .

  • If the frequency is high enough and reaches the threshold, a specified number of are ejected from the metal.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-xMfP7vOzibGj.gif?alt=media&token=728bdc25-82a2-4000-af5b-49e5c7a7d1d8

Image Courtesy of Google; you can see here that only photons that reach the given threshold of -2.0 eV can eject an electron from this metal, potassium.

We'll go over this concept in greater depth in unit three of the AP Chemistry curriculum.

Photoelectron Spectroscopy (PES)

Photoelectron spectroscopy (PES) is a technique used to compare the relative energies of atoms, ions, and molecules. PES uses energy from emitted through the to provide insight into the electronic configuration of a sample.

How does PES work?

When light of a certain frequency shines upon a sample, a limited number of are emitted. The released energy reflects the energy or energy levels within an atom. 

In viewing the photoelectron spectrum of an element, you are also able to:

  • Distinguish the different in an atom

  • Determine the of an atom.

Each peak in a photoelectron spectrum represents a different orbital level where can be found.

Here is a diagram putting all of these concepts together, but don't worry, we'll break it down further! 🎉

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-IhReCZoQ1akR.png?alt=media&token=05ad2e04-e165-4ed5-9598-7b75205075e3

Image Courtesy of Chemdx

Interpreting a Photoelectron Spectrum

Here is a photoelectron spectrum of without the markups which is how the AP exam would give you a graph like this. Let's dissect it.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-OmBxHLTMFO1l.png?alt=media&token=613bfdd9-2656-4ee1-b0ec-724e0d844605

Image Courtesy of Chemmybear

The Axes of a PES

First, let's look at the axes. When looking at a graph for the first time, the first thing you want to look at is what the graph is representing.

The x-axis is the , which is used very similarly to the term "" on the AP Chemistry exam. We'll go over ionization energy in the next study guide, but for now, think of it as the amount of energy required to remove an electron from an atom.

The closer an electron is to the of an atom, the more energy will be required to remove it. Therefore, the , or , will be higher as well. Think about this with regard to the fact that positive charges attract negative charges. The super-positive is going to be strongly attracted to the negative around it. that are closer to the are thus more strongly attracted to it.

This information should be able to tell us which side the is on in this diagram. With this photoelectron spectrum of , it is on the left side because the is greatest there (1000>0.1). So let's read the diagram from left to right.

The y-axis of this graph simply tells you how many there are in each peak.

The Peaks on a PES

Since peaks represent an orbital where can be found, the first orbital (closest to the ) must be 1s. Because the graph goes up to 2 on the y-axis, there are 2 in the . This should make sense because there is a maximum of two in the s suborbital.

The next orbital has to be 2s and the PES indicates there are 2 in this orbital as well.

So far, the seems to be 1s^2 2s^2.

There is one more peak though, which corresponds to the . However, this orbital isn't filled to maximum capacity, there are only 2 in it.

The full of this element is 1s^2 2s^2 2p^2. If I didn't tell you that this PES was for , you should be able to guess it given the graph and the periodic table.

Big Ideas with Photoelectron Spectroscopy

When breaking down a PES,

  • The position of the peak indicates how much energy is required to remove an electron from that sublevel.

  • The height of the peak indicates how many occupy that sublevel.

Practice MCQs

The next two questions are adapted from a Quizizz that kkehesci created.

  1. Refer to the photoelectron spectrum of neon shown below to answer the following question. Which of the following statements best accounts for peak A being to the left of peaks B and C?

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-7vN4jkEwOIVy.JPG?alt=media&token=92a83d1a-d86b-49fc-b3b3-7125f7f28d99

a. The of neon is 1s^2 2s^2 2p^6.

b. Neon has 8 located in its valence shell.

c. Core of an atom experience a much greater attraction to the than valence .

d. Peaks B and C show 1st ionization energies (I.E.) in neon, whereas peak A shows the 2nd I.E. of Neon.

2. Which peak shows closest to the ? A, B, C, or D?

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-gQTFZBKdv3Rh.JPG?alt=media&token=22a355f8-f21d-4eb5-9e69-da4bccea0f94

Answers to MCQs

  • The answer to #1 is C: core of an atom experience a much greater attraction to the than valence . This goes back to the concept that closest to the have a higher /.

  • The answer to #2 is peak A. This goes back to that same exact concept. If asked about which peak corresponds to the energies of the valence , you should say peak D (since they are furthest from the ).

AP Practice Question - 2019 #5

This question is taken from the AP Chemistry Exam in 2019.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-vYbo9p2LSU6V.JPG?alt=media&token=faaeb9e3-4535-424f-b262-c48f8790bc0b

In part a, they are asking you to simply write the and identify the element. We just did this a few times! If you feel comfortable with this, try it on your own first before looking at the answer.

Since the is the largest on the left, the peak on the left is the . The is:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-c9Hr7nMToV5W.JPG?alt=media&token=a4347fc2-4fc7-4403-a568-4f0a5fb3805d

You could use the noble gas shortcut here as well, but I often leave the like this when given a PES. You may make a mistake when trying to write out the noble gas shortcut with a photoelectron spectrum.

To identify the element, just pull out your periodic table! You should get Ca.

🎥 Watch Jacob Jeffries explain the parts of the atom and the experiments scientists use to study them.

Key Terms to Review (24)

1s Orbital

: The 1s orbital is closest orbital to nucleus in an atom. It can hold up to two electrons and has spherical shape.

2p Orbital

: The 2p orbital refers to the three atomic orbitals found on the second energy level (n=2), each with two lobes pointing in different directions along x,y,z axes respectively.

2s Orbital

: The 2s orbital is a type of atomic orbital, or region where an electron can exist within an atom. It's part of the second energy level (n=2) and has a spherical shape.

Albert Einstein

: Albert Einstein was a theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics. His work is also known for its influence on the philosophy of science.

Binding Energy

: Binding energy is the energy required to disassemble a whole system into separate parts. In chemistry, it often refers to the energy needed to remove an electron from an atom.

Boron

: Boron is a chemical element with the symbol B and atomic number 5. It's a metalloid, which means it has properties of both metals and non-metals.

Carbon

: Carbon is a chemical element with symbol C and atomic number 6. It's nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds.

Electron Configuration

: Electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure.

Electrons

: Electrons are subatomic particles with a negative electric charge. They orbit around the nucleus of an atom in specific energy levels or shells.

Frequency Of Light

: The frequency of light refers to the number of wave cycles that pass a given point per unit time. It determines color in visible light; high-frequency appears violet while low-frequency appears red.

Heisenberg's Uncertainty Principle

: Heisenberg's Uncertainty Principle states that it is impossible to simultaneously measure the exact position and momentum (velocity times mass) of a particle with absolute certainty.

Ionization Energy

: Ionization energy is the amount of energy required to remove an electron from a gaseous atom or ion.

Neutrons

: Neutrons are subatomic particles found in the nucleus of an atom. They have no electric charge and a mass slightly larger than that of a proton.

Nucleus

: The nucleus is at the center of an atom consisting mainly of protons and neutrons. It carries most of an atom's mass but occupies only a tiny space compared to the total size of the atom.

Orbital Levels

: Orbital levels refer to regions around an atom's nucleus where electrons are most likely found. They're often referred to as "energy levels" because each level corresponds with specific amounts of energy.

Photoelectric Effect

: The photoelectric effect refers to when electrons are ejected from matter after absorbing photons (light particles).

Photoelectron Spectroscopy (PES)

: Photoelectron Spectroscopy (PES) is a technique used to determine the energy levels of electrons in atoms or molecules. It involves shining light onto a sample and measuring the kinetic energy of the ejected electrons.

Photon

: A photon is a particle of light defined as a discrete bundle (or quantum) of electromagnetic (or light) energy. Photons are always in motion and, in vacuum, travel at a constant speed to all observers.

Principle Energy Level

: The principle energy level of an atom refers to the major energy levels, or shells, where electrons reside. These are denoted by the numbers 1, 2, 3 and so on.

Properties of Light

: The properties of light refer to the characteristics and behaviors that light exhibits, including reflection, refraction, interference, diffraction, polarization, and photoelectric effect.

Protons

: Protons are positively charged subatomic particles found within atomic nuclei.

Quantum-Mechanical Model

: The quantum mechanical model is based on quantum theory, which says matter also has properties associated with waves. It describes electrons as they move around the nucleus within regions called electron clouds or orbitals.

Subshells

: Subshells are a division of electron shells separated by different quantum numbers. They are designated as s, p, d, and f.

Wave-Particle Duality

: Wave-particle duality is the concept that all particles exhibit both wave-like and particle-like properties.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.