Use the quantized energy expression of a “particle in a box” for the following problem. Imagine...
Use the quantized energy expression of a “particle in a box” for the following problem. Imagine a “linear” conjugated molecule that has a length of 576 pm. To the nearest ones, what is the wavelength of EM radiation (in nm) that will excite a pi electron from n = 4 to the next higher quantum level (i.e., n = 4 +1)? Some helpful information: En = h2n2/(8mea2), where En is the energy of the particle (electron) at the nth quantum level (where n is a positive integer starting at 1, which corresponds to the energy level of interest), h is Planck’s constant (6.626 x 10-34 JLaTeX: \cdot ⋅ s), me is the mass of an electron (9.109 x 10-31 kg), and a is the length of the “box”, which in the present case is the length of the conjugated molecule. You may also need the speed of light, c, which is 3 x 108 m/s.
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Use the quantized energy expression of a “particle in a box” for
the following problem. Imagine...
What is the probability of finding a particle between x = 0 and x = 0.25...
What is the probability of finding a particle between x = 0 and x = 0.25 nm in a box of length 1.0 nm in (a) its lowest energy state (n = 1) and (b) when n = 100. Relate your answer to the correspondence principle. This is an illustration of the correspondence principle, which states that classical mechanics emerges from quantum mechanics as high quantum numbers are reached. What does this all mean? • Only certain (discrete) energies are...
Question # 1: Find the unit of energy in the energy expression of a free particle...
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
4. In a butadiene molecule (shown below) the pi electrons are conjugated over three bonds, which...
4. In a butadiene molecule (shown below) the pi electrons are conjugated over three bonds, which can be approximated as a particle in a box. Calculated the wavelength of light needed to excite an electron from the n=2 to n=3 level, taking the box length to be 5.6 Angstroms.
7. π electron is an electron which resides in the pi bond(s) of a double bond or a triple bond, o...
7. π electron is an electron which resides in the pi bond(s) of a double bond or a triple bond, or in a conjugated p orbital. The 1,3,5-hexatriene molecule is a conjugated molecule with 6 t electrons. Consider the Tt electrons free to move back and forth along the molecule through the delocalized pi system. Using the particle in a box approximation, treat the carbon chain as a linear one-dimensional "box". Allow each energy level in the box to hold...
Quantized and total photon energy The particle characteristics of electromagnetic radiation are responsible for the quantized...
Quantized and total photon energy The particle characteristics of electromagnetic radiation are responsible for the quantized behavior of light energy. This behavior explains the results of varying the intensity and wavelength for an observed photoelectric effect, which describes the emission of electrons when light shines on a metal surface. If light only exhibited a purely wavelike behavior, then either increasing the intensity or decreasing the wavelength would both increase the rate at which electron are emitted. However, monochromatic light of...
problems 7 & 8 Problem 7: A particle confined in a rigid one-dimensional box of length...
problems 7 & 8
Problem 7: A particle confined in a rigid one-dimensional box of length 1 x 10-14m has an energy level ER = 32 MeV and an adjacent energy level En+1 = 50 MeV. 1 MeV = 1 x 106 eV (a) Determine the values of n and n + 1. Answer: n = 4 and n+1 = 5. (b) What is the wavelength of a photon emitted in the n+1 to n transition? Answer: X = 6.9...
NAME Physical Chemistry Test 2 Instructions: Do FIVE of the following problems Your best problem ...
6,7,8
NAME Physical Chemistry Test 2 Instructions: Do FIVE of the following problems Your best problem will be graded out of points Your third best will be graded out of 20 points Your fifth best will be graded out of 10 peints f30 pointsYour second best will be graded out of 25 points Your fourth best will be graded out of 15 points 1. The work function of uranium is 3.73 ev a. Caculate the maximum photon wavelength needed to...
The energy levels for a particle in a 1-D box of dimension (L) is provided by...
The energy levels for a particle in a 1-D box of dimension (L) is provided by the following expression: n h2 E, 2mL2 where m is the mass of the particle, h-bar = h/2 andn is the quantum number. Evaluate the energy associated with the first level (n 1) for an argon atom in a 10 A 1-D box. Select one: a. 8.27 x 10-25 kJ/mol b. 4.98 x 10 1 kJ/mol c. 8.27 x 1028 kJ/mol d. 4.98 x...
Question 3: Quantum (10 pts) The quantum energy levels of an electron in a box of...
Question 3: Quantum (10 pts) The quantum energy levels of an electron in a box of length of Lare given by En = n2h2/8mL2 where n = 1, 2, 3, ..., h is Planck's constant and m is the mass of an electron. What is the smallest value that I can have if an excited electron in the box possibly produces visible light? Give you answer in units of meters or nanometers.
The electronic spectrum of the molecule butadiene, CH2=CH-CH=CH2, can be approximated using the one dimensional particle-in-a-box...
The electronic spectrum of the molecule butadiene, CH2=CH-CH=CH2, can be approximated using the one dimensional particle-in-a-box if one assumes that the conjugated double bonds span the entire four-carbon chain. If the electron absorbing a photon have wavelength 2170 Angstroms is going from the level n = 2 to the level n = 3, what is the approximate length of the C.He molecule? (The experimental value is -4.8 Angstrom.) length 2 5 .74*10-10
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
4. In a butadiene molecule (shown below) the pi electrons are conjugated over three bonds, which can be approximated as a particle in a box. Calculated the wavelength of light needed to excite an electron from the n=2 to n=3 level, taking the box length to be 5.6 Angstroms.
7. π electron is an electron which resides in the pi bond(s) of a double bond or a triple bond, or in a conjugated p orbital. The 1,3,5-hexatriene molecule is a conjugated molecule with 6 t electrons. Consider the Tt electrons free to move back and forth along the molecule through the delocalized pi system. Using the particle in a box approximation, treat the carbon chain as a linear one-dimensional "box". Allow each energy level in the box to hold...
Quantized and total photon energy The particle characteristics of electromagnetic radiation are responsible for the quantized behavior of light energy. This behavior explains the results of varying the intensity and wavelength for an observed photoelectric effect, which describes the emission of electrons when light shines on a metal surface. If light only exhibited a purely wavelike behavior, then either increasing the intensity or decreasing the wavelength would both increase the rate at which electron are emitted. However, monochromatic light of...
problems 7 & 8
Problem 7: A particle confined in a rigid one-dimensional box of length 1 x 10-14m has an energy level ER = 32 MeV and an adjacent energy level En+1 = 50 MeV. 1 MeV = 1 x 106 eV (a) Determine the values of n and n + 1. Answer: n = 4 and n+1 = 5. (b) What is the wavelength of a photon emitted in the n+1 to n transition? Answer: X = 6.9...
6,7,8
NAME Physical Chemistry Test 2 Instructions: Do FIVE of the following problems Your best problem will be graded out of points Your third best will be graded out of 20 points Your fifth best will be graded out of 10 peints f30 pointsYour second best will be graded out of 25 points Your fourth best will be graded out of 15 points 1. The work function of uranium is 3.73 ev a. Caculate the maximum photon wavelength needed to...
The energy levels for a particle in a 1-D box of dimension (L) is provided by the following expression: n h2 E, 2mL2 where m is the mass of the particle, h-bar = h/2 andn is the quantum number. Evaluate the energy associated with the first level (n 1) for an argon atom in a 10 A 1-D box. Select one: a. 8.27 x 10-25 kJ/mol b. 4.98 x 10 1 kJ/mol c. 8.27 x 1028 kJ/mol d. 4.98 x...
Question 3: Quantum (10 pts) The quantum energy levels of an electron in a box of length of Lare given by En = n2h2/8mL2 where n = 1, 2, 3, ..., h is Planck's constant and m is the mass of an electron. What is the smallest value that I can have if an excited electron in the box possibly produces visible light? Give you answer in units of meters or nanometers.
The electronic spectrum of the molecule butadiene, CH2=CH-CH=CH2, can be approximated using the one dimensional particle-in-a-box if one assumes that the conjugated double bonds span the entire four-carbon chain. If the electron absorbing a photon have wavelength 2170 Angstroms is going from the level n = 2 to the level n = 3, what is the approximate length of the C.He molecule? (The experimental value is -4.8 Angstrom.) length 2 5 .74*10-10
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