Activity Manual 22 on Photons does not discuss the momentum of a photon, but the photon’s...
Activity Manual 22 on Photons does not discuss the momentum of a photon, but the photon’s momentum and momentum conservation are important for Positron Emission Tomography, a medical imaging technique that you will be studying in class soon. So in this homework you will learn about photon momentum and momentum conservation in the context of photon emission from hydrogen atoms. To remind you, in Physics 101 you learned that the momentum ~p of an object with mass m traveling with velocity ~v is given by ~p = m~v. The magnitude of the momentum of a photon has been found to be given by |~pphoton| = h/λ, where h is Planck’s constant and λ is the photon’s wavelength. The direction of the photon’s momentum is the direction in which the photon is moving. Suppose that a hydrogen atom that is initially at rest and in its n = 6 level makes a transition to its n = 1 level, emitting a photon in the process.
(a) What is the energy (in Joules) of the emitted photon?
(b) What is the wavelength (in meters) of the emitted photon?
(c) Assuming that the total momentum of the system is conserved, what is the speed with which the hydrogen atom is traveling after the photon has been emitted?
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Activity Manual 22 on Photons does not discuss the momentum of a
photon, but the photon’s...
To remind you, in Physics 101 you learned that the momentum ~p of an object with...
To remind you, in Physics 101 you learned that the momentum ~p of an object with mass m traveling with velocity ~v is given by ~p = m~v. The magnitude of the momentum of a photon has been found to be given by |~pphoton| = h/λ, where h is Planck’s constant and λ is the photon’s wavelength. The direction of the photon’s momentum is the direction in which the photon is moving. Suppose that a hydrogen atom that is initially...
A hydrogen atom initially in its ground state i.e., n= 1 level, absorbs a photon and...
A hydrogen atom initially in its ground state i.e., n= 1 level, absorbs a photon and ends up in n= 3 level. What must have been the frequency of the incident photon? (b) Now the electron makes spontaneous emission and comes back to the ground state. What are the possible frequencies of the photons emitted during this process?
d u momentum of the emitted photon. 7. [15-22) (a) [5] How many photons are there...
d u momentum of the emitted photon. 7. [15-22) (a) [5] How many photons are there is 1 J of light at a wavelength of X-500 nm? (b) [5] Why is there a cutoff frequency for electromagnetic radiation below which electrons are not emitted from a metal. (b) [5-12] Explain how it is that Einstein's explanation of the photoelectric effect is in conflict with basic notions of classical physics and how it is that this explanation leads to totally new...
6. A stream of laser photons with a frequency of 3.0x1015 Hz excited electrons in the...
6. A stream of laser photons with a frequency of 3.0x1015 Hz excited electrons in the lowest energy of the hydrogen atom shown in the energy level diagram below Energy a. Show to what level the photon excited the electron. -6.02x10-20 -8.72x10 b. Show all the possible emission transitions as the 1.36x10-19J state. tron returns from the n = 3 energy level to the ground 242x1-19 c. Calculate AE for each line produced in b. -5.45x1019 -2.18x101 d. What is...
Activity 26-5. Atomic spectra [Accompanies Section 26-5] A certain type of atom (not hydrogen) has three...
Activity 26-5. Atomic spectra [Accompanies Section 26-5] A certain type of atom (not hydrogen) has three energy levels numbered 1, 2, and 3, as shown in the upper illustration. There are three possible transitions between these levels that lead to emission of a photon: 3 → 1, 3 → 2, and 2 → 1. The lower illustration shows the emission spectrum from a gas of these atoms. There are three emission lines, A, B, and C. (a) Rank the photons...
A certain type of atom (not hydrogen) has three energy levels numbered 1, 2, and 3,...
A certain type of atom
(not hydrogen) has three energy levels numbered 1, 2, and
3, as shown in the upper illustration. There are three possible
transitions between these levels that lead to emission of a photon:
3 ® 1, 3 ® 2, and 2 ® 1.
The lower illustration shows the emission spectrum from a gas of
these atoms. There are three emission lines, A, B, and C.
(a) Rank the photons emitted in the transitions 3 ®...
Consider a photoelectric effect experiment. Calculate the minimum photon energy needed to produce photoelectrons for the...
Consider a photoelectric effect experiment. Calculate the minimum photon energy needed to produce photoelectrons for the following metals: Sodium Aluminum Platinum For the photon energies you calculated in problem #1, calculate the wavelength and frequency for each. In what part of the electromagnetic spectrum do these photons belong? Calculate the radii and energies of the first three allowed orbits for the Bohr Model of the hydrogen atom in both joules and electron-volts. Show your work. Calculate the energies of photons...
1. Thinking about electrons and photons, what is emission? A. An electron interacting with a photon...
1. Thinking about electrons and photons, what is emission? A. An electron interacting with a photon to reach a higher energy level B. An electron releasing a photon to reach a lower energy level C. A photon releasing an electron to reach a lower energy level 2. Rank the following in INCREASING wavelength (smallest to largest): green light, infrared, micro waves, X-ray A. green light, micro waves, infrared, X-ray B. micro waves, infrared, green light, X-ray C. X-ray, green light,...
1. Does the fact that the speed of light is a definite, predictable quantity conflict with...
1. Does the fact that the speed of light is a definite, predictable quantity conflict with the uncertainty relations? 2. How could you tell if electrons in very distant galaxies obey the Pauli exclusion principle? 3. Calculate the maximum wavelength for the initiation of a photoelectric current in the aluminum (work function W = 4.28 eV). (Answer: 290 nm) 4. An electron in the hydrogen atom drops from the n=5 level to the n=1 level. What are the frequency, wavelength,...
33.8 Problems biting the atom drops from an energy level of Ei--10.64 eV to an energy...
33.8 Problems biting the atom drops from an energy level of Ei--10.64 eV to an energy level of 12.70 eV 33.1 A photon is emitted by an atom when one of the electrons or- (a) What is the energy of this photon (in eV)? (b) What is the energy of this photon (in D? (c) What is the frequency of this photon? (d) What is the wavelength of this photon? (e) What is the momentum of this photon? 33.2 The...
d u momentum of the emitted photon. 7. [15-22) (a) [5] How many photons are there is 1 J of light at a wavelength of X-500 nm? (b) [5] Why is there a cutoff frequency for electromagnetic radiation below which electrons are not emitted from a metal. (b) [5-12] Explain how it is that Einstein's explanation of the photoelectric effect is in conflict with basic notions of classical physics and how it is that this explanation leads to totally new...
6. A stream of laser photons with a frequency of 3.0x1015 Hz excited electrons in the lowest energy of the hydrogen atom shown in the energy level diagram below Energy a. Show to what level the photon excited the electron. -6.02x10-20 -8.72x10 b. Show all the possible emission transitions as the 1.36x10-19J state. tron returns from the n = 3 energy level to the ground 242x1-19 c. Calculate AE for each line produced in b. -5.45x1019 -2.18x101 d. What is...
A certain type of atom
(not hydrogen) has three energy levels numbered 1, 2, and
3, as shown in the upper illustration. There are three possible
transitions between these levels that lead to emission of a photon:
3 ® 1, 3 ® 2, and 2 ® 1.
The lower illustration shows the emission spectrum from a gas of
these atoms. There are three emission lines, A, B, and C.
(a) Rank the photons emitted in the transitions 3 ®...
Consider a photoelectric effect experiment. Calculate the minimum photon energy needed to produce photoelectrons for the following metals: Sodium Aluminum Platinum For the photon energies you calculated in problem #1, calculate the wavelength and frequency for each. In what part of the electromagnetic spectrum do these photons belong? Calculate the radii and energies of the first three allowed orbits for the Bohr Model of the hydrogen atom in both joules and electron-volts. Show your work. Calculate the energies of photons...
1. Thinking about electrons and photons, what is emission? A. An electron interacting with a photon to reach a higher energy level B. An electron releasing a photon to reach a lower energy level C. A photon releasing an electron to reach a lower energy level 2. Rank the following in INCREASING wavelength (smallest to largest): green light, infrared, micro waves, X-ray A. green light, micro waves, infrared, X-ray B. micro waves, infrared, green light, X-ray C. X-ray, green light,...
33.8 Problems biting the atom drops from an energy level of Ei--10.64 eV to an energy level of 12.70 eV 33.1 A photon is emitted by an atom when one of the electrons or- (a) What is the energy of this photon (in eV)? (b) What is the energy of this photon (in D? (c) What is the frequency of this photon? (d) What is the wavelength of this photon? (e) What is the momentum of this photon? 33.2 The...
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