AP Physics B 2013 Question 7 - Modern Physics - Energy Levels

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24 Apr 201505:36

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TLDRThis script from the 2013 AP Physics B exam explores a modern physics question on atomic energy levels. It discusses a hypothetical atom with electrons transitioning from level 3 to 1, emitting photons of varying energies. The focus is on calculating the longest wavelength photon, which corresponds to the lowest energy transition (3 to 2). The ionization energy of the atom is also covered, highlighting that only photons with quantized energy can excite electrons. Finally, it explains the effects of incident photons with 11 eV and 14 eV on the atom, emphasizing that only sufficient energy leads to ionization, with excess energy converted into kinetic energy.

Takeaways

📊 This problem is from the 2013 AP Physics B exam and deals with atomic energy levels.
🔬 The energy level diagram provided is for a hypothetical atom.
💡 Electrons in the n=3 level undergo transitions resulting in photon emission.
➡️ Possible transitions are 3 to 1, 3 to 2, and then 2 to 1.
📏 The longest wavelength of photons is associated with the lowest energy transition, which is from 3 to 2.
📉 Energy levels: 3 to 2 is 2.25 eV, 3 to 1 is 9 eV, and 2 to 1 is 11.25 eV.
📐 Using the formula λ = hc/E, the longest wavelength is calculated to be 551 nm.
⚡ The ionization energy of the atom in the ground state is 12 eV.
🔵 Photons of 11 eV will not interact with electrons in the n=1 state because the energy is not quantized correctly.
💥 Photons of 14 eV will ionize the atom, causing the electron to be ejected and leaving it with 2 eV of kinetic energy.

Q & A

What type of question is number seven from the 2013 AP Physics B exam?
-It is a modern physics style question dealing with atomic energy levels.
What is provided in the question's diagram?
-An energy level diagram for a hypothetical atom.
What transitions are being analyzed in this question?
-Transitions of electrons from the n = 3 level to the n = 1 level with photon emission.
How many possible transitions can electrons undergo from the n = 3 level?
-There are three possible transitions: directly from 3 to 1, from 3 to 2 and then 2 to 1.
What is the relationship between photon wavelength and energy?
-Energy is directly related to frequency and inversely related to wavelength, so a longer wavelength corresponds to lower energy.
Which transition results in the longest wavelength of emitted photons?
-The transition from 3 to 2 results in the longest wavelength because it is associated with the lowest energy level transition.
How is the wavelength of the photon calculated?
-The wavelength is calculated using the formula λ = hc / E, where h is Planck's constant, c is the speed of light, and E is the energy of the transition.
What is the ionization energy of the atom in the ground state?
-The ionization energy of the atom in the ground state is 12 electron volts (EV).
What happens when photons of 11 EV are incident on the atom in the ground state?
-Nothing happens because 11 EV is not enough to excite the electron from the ground state since there is no energy level corresponding to 1 EV above the ground state.
What is the effect of shining 14 EV photons on the atom?
-Shining 14 EV photons on the atom ionizes it, causing the electron to be ejected with 2 EV of kinetic energy.

Outlines

00:00

🔬 Understanding Atomic Transitions and Photon Emission

This paragraph explains a problem from the 2013 AP Physics B exam, focusing on modern physics and atomic energy levels. The task involves analyzing an energy level diagram for a hypothetical atom and identifying possible transitions for electrons initially in the n=3 level. The electrons can either transition directly from n=3 to n=1 or go through an intermediate level (n=2) before reaching n=1, resulting in photon emission. The paragraph emphasizes the three possible transitions and their corresponding photon energies.

05:01

📏 Calculating Longest Wavelength of Emitted Photons

This paragraph discusses how to calculate the longest wavelength of photons emitted by the atom. The longest wavelength corresponds to the lowest energy transition, which occurs from n=3 to n=2. The energy of this transition is given as 2.25 eV. Using the energy-wavelength relationship (λ = hc/E), the wavelength is calculated to be 551 nanometers. The paragraph also explains how to handle unit conversions using constants provided in the AP Physics reference materials.

⚡ Determining Ionization Energy from the Ground State

Here, the focus shifts to calculating the ionization energy of the atom from its ground state. The ionization energy is defined as the energy required to remove an electron completely, which in this case is 12 eV. The explanation is straightforward, noting that this value corresponds to the energy needed to move an electron from the ground state to an infinite level, effectively removing it from the atom.

❌ Ineffective Photon Energy for Electron Excitation

This paragraph examines the effect of 11 eV photons on electrons in the n=1 (ground) state. It is explained that for an electron to be excited, the energy of the incident photon must match the energy difference between allowed energy levels. Since 11 eV does not correspond to any available transition from the ground state, no excitation occurs, and the photon passes through the atom without interacting with the electron.

💥 Photon-Induced Ionization of the Atom

In the final paragraph, the discussion covers what happens when a 14 eV photon interacts with the atom. This energy is sufficient to ionize the atom, meaning it will remove an electron completely. The paragraph notes that the excess energy, beyond what is needed for ionization (12 eV), will be converted into kinetic energy for the ejected electron, resulting in the electron having 2 eV of kinetic energy after ionization.

Mindmap

Keywords

💡Energy Levels

Energy levels refer to the fixed amounts of energy that electrons in an atom can have. In the video, the concept of energy levels is crucial as the electrons transition between these levels, emitting photons in the process. For example, transitions from n=3 to n=1 or n=2 are discussed.

💡Photon Emission

Photon emission occurs when an electron moves from a higher energy level to a lower one, releasing energy in the form of a photon. This concept is central to the problem discussed, as electrons transitioning to lower energy levels in the atom emit photons.

💡Wavelength

Wavelength is the distance between successive peaks of a wave, often related to light or other electromagnetic radiation. In the video, calculating the longest wavelength of emitted photons involves understanding the relationship between energy, frequency, and wavelength.

💡Ionization Energy

Ionization energy is the amount of energy required to remove an electron from an atom in its ground state. The video explains how the ionization energy of the atom in the ground state is 12 electron volts (eV), which is the energy needed to ionize the atom.

💡Electron Volt (eV)

An electron volt (eV) is a unit of energy equal to approximately 1.6 x 10^-19 joules. It's used to measure the energy levels of electrons in atoms. The video frequently uses eV to describe the energy differences between levels and the energy of photons.

💡Transition

A transition refers to the movement of an electron from one energy level to another within an atom. The video outlines possible transitions for electrons starting in the n=3 level and ending in the n=1 level, including direct and stepwise transitions.

💡Ground State

The ground state is the lowest energy state of an atom or particle. In the video, the ground state is referenced when discussing the final energy level (n=1) to which electrons transition and the energy required to ionize the atom from this state.

💡Excitation

Excitation is the process of an electron moving to a higher energy level after absorbing energy. The video mentions that photons of 11 eV are insufficient to excite an electron from the n=1 state because there is no corresponding energy level available.

💡Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. In the context of the video, when photons with more energy than the ionization energy (14 eV) hit the atom, the excess energy is converted into kinetic energy for the ejected electron.

💡Quantized Energy

Quantized energy means that energy levels are discrete rather than continuous. The video explains how electrons need exact amounts of energy to move between specific energy levels, reflecting the quantized nature of atomic energy levels.

Highlights

Introduction to the modern physics question on atomic energy levels.

Energy level diagram is for a hypothetical atom with unknown identity.

Electrons start in the n = 3 energy level and transition to n = 1, emitting photons.

Possible transitions include 3 to 1 directly or 3 to 2, then 2 to 1.

Longest wavelength is associated with the lowest energy transition.

Energy level transition from 3 to 2 has an energy of 2.25 electron volts (eV).

Energy transition 3 to 1 is 11.25 eV, and 3 to 2 is 9 eV.

Calculate wavelength using the formula λ = hc/E, where h is Planck's constant and c is the speed of light.

Using hc = 1240 eV·nm to find the wavelength in nanometers.

Calculated wavelength for the transition from 3 to 2 is 551 nanometers.

Ionization energy in the ground state is 12 eV.

Photons with 11 eV incident on n = 1 state do not have the required energy to excite electrons.

Photons of 11 eV pass through without interacting as there is no matching energy level.

14 eV photons are sufficient to ionize the atom, ejecting the electron.

Excess energy from 14 eV photons appears as 2 eV of kinetic energy for the ejected electron.

Transcripts

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