-1/2 6) For a particle on a ring with the wavefunction: () = π cos() calculate the average z-component of the angular momentum of the particle using the operator L = - th 2 Loshould be o -1/2 (0) = π cos (4) L₂= - iħ d dø 2 t =√x² L₂ O L₂ Ydo L.

-1/2 6) For a particle on a ring with the wavefunction: () = π cos() calculate the average z-component of the angular momentum of the particle using the operator L = - th 2 Loshould be o -1/2 (0) = π cos (4) L₂= - iħ d dø 2 t =√x² L₂ O L₂ Ydo L.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.26E: For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the...

See similar textbooks

Related questions

Q: Li+ find the configuration

A: Electronic configuration: Electronic configuration can be define as the arrangement of electrons…

Q: 1. Calculate the pH of a 5.8 x 10-8 M solution of KOH(aq) at 25 °C. Report the answer to the…

A: Note: As per our guidelines, we are supposed to answer only one question when multiple questions are…

Q: 9. Measurement of Acetylcholine Levels by pH Changes You have a 15 mL sample of acetylcholine (a…

A: Given data 15ml volume PH= 7.65 After decreases PH = 6.87 Find nanomol

Q: 5) Draw all products of the following reaction and determine which one (s) are the major products:…

A: -> Dimethyl Sulphur oxide (DMSO) is polar aprotic solvent.In presence of this solvent there occur…

Q: The solubility of SrCO3 in water at 25 °C is measured to be 0.0045 Round your answer to 2…

A: Given the solubility of SrCO3, in water at 25 °C is 0.0045 g/L We have to calculate Ksp of SrCO3…

Q: When cycloocta-1,3-diene reacts with 1 mol HCI, which structure/s correspond/s to the 1,2-addition…

A: Here we are required to find the major product of the reaction between cycloocta1,3 diene and 1 mol…

Q: Question: The vapor pressure curve for ethanol (CH₂CH₂OH) and water (H₂O) is described by the…

A: P(C2H5OH) = 108.04494-1554322265+T(K)let a= 22265 + Tb= 1554322265+Tc=8.04494-b

Q: Assume that you have a variety of cyclohexanes substituted in the positions indicated. Identify the…

A: Here we are required to find the position of the group present on the cyclohexane.

Q: Calculate the pH of a weak base solution (quadratic equation). Calculate the pH of a 0.0295 M…

Q: b) H Br Br Br₂ VS. Į

A: Reaction (a) is electrophilic addition reaction of alkene which is directed by stereochemistry of…

Q: An unknown compound has the following chemical formula: Fe(NO3) where x stands for a whole number.…

Q: Consider the following molecular-level diagram of a chemical reaction between N₂(g) and Cl₂(g). The…

A: Balanced chemical equation is the chemical equation having equal number of each type of atoms on…

Q: Peak A has a height of 172 mm and a width at half height of 14.7 mm. Peak B has a height of 85 mm…

A: Given :- Height of Peak A = h = 172 mm Width of Peak A at half height = w1/2 = 14.7 mm Height of…

Q: Molecule CO₂ SO₂ CH4 PCI5 NH3 BrF3 SF4 CIF3 Lewis Structure (Insert photo of handwritten answer)…

A: This can be explained by the VSEPR Theory. So following observation are observed:-

Q: Balanced Equation: CH3COOH(aq) + NaHCO3 →

A: In this question, we will balanced the incomplete equation. In this equation, Acetic acid is acidic…

Q: how can i find the kps given the pH?

Q: = O KINETICS AND EQUILIBRIUM Using the general properties of equilibrium constants At a certain…

A: The balanced equilibrium reaction is: H2(g) + Cl2(g) ⇌ 2HCl(g) ; K = 9.53*10-5 Equilibrium constant…

Q: What is the formula to calculate the concentration of BSA in the sample. The absorption coefficient…

Q: Determine the standard heat of each of the following reactions at 25°C: 3NO2(g) + H2O(l) → 2HNO3(l)…

Q: A chemist measures the amount of oxygen gas produced during an experiment. She finds that 95.5 g of…

Q: Use the References to access important values if needed for this question. What volume of a 0.274 M…

A: Potassium hydroxide reacts with hydroiodic acid, to form potassium iodide and water. The equation…

Q: The Kp for the reaction A (g) ⇌ 2 B (g) is 0.0670. What is Kp for the reaction 2 A (g) ⇌ 4 B (g)?

A: As we know, If the equation (having equilibrium constant K) is multiplied by 2, the equilibrium…

Q: Question. Determination of percent water (%H₂O) in hydrated FeSO4nH₂O is demonstrated in General…

A: The given data is- Group number Mass of hydrated salt (g) Mass of anhydrous salt (g) 1 3.38 1.4…

Q: Calculate the solubility of PbCrO4 in water at 25 °C. You'll find Kp data in the ALEKS Data tab. sp…

A: Solubility of PbCrO4 = ..... g/L Ksp = 2.00 x 10-14 Molar mass of PbCrO4 = 323.19 g/mol

Q: Try Again Your answer is incorrect. • BP: The name of this compound is not "boron phosphide". Be…

A: The name of the compound involves words like mono, di , tri etc. Depending on the number of atoms…

Q: Answer the questions below for the reaction of lithium with oxygen: 4 Li (s) + O₂(g) →2 Li₂0 (s) a)…

A: A neutral atom always show "no charge". Cation bears "+ve charge" Anion bears "-ve charge". A…

Q: You were asked to determine the acid content of vinegar and soda samples. You performed a simple…

A: Given, Molecular mass of KHP =204.22gmol

Q: Exercise 4: Commercial acids and bases are aqueous solution with following properties, Calculate the…

A: Molarity : It is defined as the number of moles of solute dissolved per litre of the solution .…

Q: How many grams of water is produced if 400 grams of CaCo3 precipotate is the produced byproduct? Use…

Q: if you wish to measure approximately 40 mL of water using the following measuring devices, if the…

A: A graduated measuring device is one that has markings. Each marked line represents a specific amount…

Q: For each pair of substrates below, choose the one that will react faster in a substitution reaction,…

Q: write the structure of ethanol

Q: Curved arrows are used to illustrate the flow of electrons. Follow the curved arrows and draw the…

A: In organic reaction mechanism curved arrows are used to show the flow of electrons. The electrons…

Q: Although both SeF4 and XeF4 have four fluorine atoms each, SeF4 has molecular geometry and is…

A: This question is related to valence shell electron pair repulsion (VSEPR) theory which is used to…

Q: a) Cu(NO3)2 + NaBr → CuBr₂ + NaNO3 - b) FeCl3 + Na₂CO3 → Fe₂(CO3)3 + NaCl c) K+H₂O2KOH + H₂ Reminde

Q: Q6. Why are peaks in HNMR split? What is the criteria for the splitting? Q7. How many signals would…

A: (1)if carbon have +ve charge then proton is deshield its ppm value is high (2)if carbon have -ve…

Q: Indicate whether the pair of structures shown represent stereoisomers, constitutional isomers,…

Q: Complete the following solubility constant expression for BaSO4. Ksp = X Ś 00

A: BaSO4 is sparingly soluble slat and we have to find out the solubility constant expression of the…

Q: Explain why the n→π* interactions contributes more to the overall stabilization of the protein than…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Prepare cyclomethine dyes (comp 4) using condensation reaction ZI H,C₂ 4 [34708-09-3] CI™

Q: Calculate the number of Li atoms in 3.1 mol of Li. Express your answer using two significant…

A: Since, Moles is the ratio of mass to the molar mass of that atom or molecules. Also, Number of atoms…

Q: For each reaction, identify the Brønsted-Lowry acid, the Brønsted-Lowry base, the conjugate acid,…

Q: Draw the major product of this solvolysis reaction. Ignore any inorganic byproducts. CI CH3CH2OH

Q: An atomic cation with a charge of +1 has the following electron configuration: 1s 2s 2p 3s 3p 3d ¹4s…

A: Since, Electronic configuration represent the electron present in orbital in which way. Arrangement…

Q: Question: The following data measures how quickly Heg) diffuses in gas chromatograph detector as…

A: From given data tables :-

Q: A 0.235 mL sample of carbon tetrachloride (density = 1.59 g/mL, MM = 153.81 g/mol) contains how many…

Q: There is a system in which solid colloids (density = 2.5 g/cm^3) with a particle diameter of 300 nm…

A: Diffusion and sedimentation in solid colloids.

Q: 1. which of the following pairs are constitutional isomers? 2. What is the IUPAC name of the…

Q: Decide which element probably forms a compound with hydrogen that has a chemical formula most and…

A: Similarity of Hydrogen with phosphours :- It formed PH3 compounds

Q: A "Unified Formula" for Degrees of Unsaturation (a.k.a "Index of Hydrogen Deficiency") C = #carbons…

A: Degree of unsaturation refers to the total number of rings and pi bonds in a molecule. This helps in…

Concept explainers

Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.

Question

<
-1/2
6) For a particle on a ring with the wavefunction: () = π cos() calculate the average
z-component of the angular momentum of the particle using the operator L = - ih
Loshould be o
V(0) = TT
-1/2
T
cos ( )
L₂=-ih d
d$
2 tr
<h₂> [p* L₂ da
0
HO
H
+
→

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Techniques and Applications of Quantum Theory

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?
Imagine a particle free to move in the x direction. Which of the following wavefunctions would be acceptable for such a particle? In each case, give your reasons for accepting or rejecting each function. (1) Þ(x) = x²; (iv) y(x) = x 5. (ii) ¥(x) = ; (v) (x) = e-* ; (iii) µ(x) = e-x²; (vi) p(x) = sinx
P7B.1 Imagine a particle confined to move on the circumference of a circle ('a particle on a ring'), such that its position can be described by an angle & in the range 0 to 2π. Find the normalizing factor for the wavefunctions: (a) e" and (b) eim, where m, is an integer.
The Hamiltonian operator y for the harmonic oscillator is given by Â = h? d? + suw? â?, where l is the reduced mass and w = 27V is the angular 2µ dæ? P[-] pwx? frequency. Is the function f(x) = x exp an eigenfunction of that Hamiltonian? 2h O No. Yes, and the eigenvalue is ħw. 2 Yes, and the eigenvalue is hw. 3ħw Yes, and the eigenvalue is 4
1:51 PM Sun Oct 9 -1/2 5) For a particle on a ring with the wavefunction: () = π kinetic energy of the particle using the operator K = -1/2 Y(0) = IT 21T K=-ħ²d² 21d² 2 cos ($) = kdo T (17¹/2)² 211 - f = "Cos (0) . # de TỈ Cos (O). t d. TỈ Cosco) do = 21 0 21 cos() calculate the average cos(0). -ħ² d² do 21 do² 10:52 @ 79% + : 5 9 +
Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction ψn. (a) Without evaluating any integrals, explain why ⟨x⟩ = L/2. (b) Without evaluating any integrals, explain why ⟨px⟩ = 0. (c) Derive an expression for ⟨x2⟩ (the necessary integrals will be found in the Resource section). (d) For a particle in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why <p2x> = n2h2/4L2.
You are given a free particle (no potential) Hamiltonian ÎI - dependent wave-functions = ₁(x, t) V₂(x, t) = -it 2h² m = ħ² d² 2m dx2 sin(27x)e-it 2 sin(x)eit + sin(2x)e¯ hn 2 • Are V₂(x, 0) eigenfunctions of Ĥ ? (give explanation for each case) and two time- -it 2hr 2 m (1) (2)
5. Consider a particle constrained to move in one dimension described by the wavefunction v (x) = Ne2** (a) Determine the normalization constant (b) Is the wavefunction an eigenfunction of d? +16x? dx? (c) Calculate the probability of finding the particle anywhere along the negative x-axis
Normalize (to 1) the wavefunction e-ax^2 in the range −∞ ≤ x ≤ ∞, with a > 0. Refer to the Resource section for the necessary integral.
Consider a 1D particle in a box confined between a = 0 and x = 3. The Hamiltonian for the particle inside the box is simply given by Ĥ . Consider the following normalized wavefunction 2m dz² ¥(2) = 35 (x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your 5832 final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectation value to the lowest energy state of the 1D particle in a box and comment on how the expectation value you calculated for the wavefunction ¥(x) is an example of the variational principle.
wavefunction iš E7D.5(b) Calculate the probability that a particle will be found between 0.65L and 0.671 in a box of length L for the case where the wavefunction is (i) Y, (ii) y.. You may make the same approximation as in Exercise E7D.5(a).
9. The ground-state wavefunction for a particle confined to a one-dimensional box of length Lis 1/2 TCX L L Suppose the box is 10.0 nm long. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm. sin en