Self-test 7B.3 As remarked in Self-test 7B.2, the normalized wavefunction of the next higher energy level of the electron in this model of the nanotube is (2/L)1/2 sin(2nx/L). What is the probability of finding the electron between x = L/4 and x = L/2? Answer: 025

Self-test 7B.3 As remarked in Self-test 7B.2, the normalized wavefunction of the next higher energy level of the electron in this model of the nanotube is (2/L)1/2 sin(2nx/L). What is the probability of finding the electron between x = L/4 and x = L/2? Answer: 025

Physical Chemistry

2nd Edition

ISBN:9781133958437

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

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

Chapter15: Introduction To Electronic Spectroscopy And Structure

Section: Chapter Questions

Problem 15.59E: Would the light from fireflies be considered an example of a fluorescence or a phosphorescence...

See similar textbooks

Related questions

Q: Determine the name of each ionic compound Li3N

Q: 19- A proposed mechanism for the reaction between iodine chloride gas and hydrogen gas is shown…

A: In balanced chemical reaction , number of atoms of each species are equal on both reactant and…

Q: Element XYZ has two isotopes: XYZ-79 (mass =69.9943 amu) and XYZ-81 (mass=80.9893 amu). If the…

A: Given,Element : XYZ XYZ-79…

Q: Imagine an alternate universe where the value of the Planck constant is 6.62607×10 J-s. In that…

Q: When a 29.2 mL sample of a 0.312 M aqueous hydrocyanic acid solution is titrated with a 0.324 M…

Q: Draw the molecular orbital (MOs) that results from combining the following atomic orbitals. Recall…

A: •Here given overlapping between:-

Q: 1.41 L he construct a graph to show the trend in the third ionization energies of the elements from…

A: We have asked to construct a graph to show the trend in the third ionization energies of the…

Q: Which of the below statements is false? O Phosphate is an important intracellular buffer. Le…

A: A buffer solution is a solution that has the ability to resist changes in pH when small amounts of…

Q: Two glass bulbs each having a volume of exactly 1L are connected by a valve. The left bulb contains…

A: The Ideal Gas Law is a fundamental relationship between the pressure, volume, temperature and the…

Q: Macmillan Learning A 6.41 L cylinder contains 1.55 mol of gas A and 3.63 mol of gas B, at a…

A: Given data : Volume of cylinder , V = 6.41 L Temperature , T = 27degrees Celsius = (27+273)K = 300…

Q: Give the structure of compounds. 1. Succinic anhydride 2. CH3 CH3 methanol hot KMnO4 Thionyl…

A: In the first reaction, succinic anhydride reacts with methanol to form an ester. In this reaction…

Q: . Give the chemical symbols of elements (1 each, although some may have more than 1 correct answer)…

A: Periodic table of elements consists of seven periods and eighteen elements are arranged in the…

Q: Metallic silver crystallizes in a face-centered cubic lattice, with one Ag atom per lattice point.…

Q: 1. Excluding hydrogen, what are the formal charges on each of the following atoms? a. b. с. d. H3C_{…

A: we have to calculate the formal charge on each atom, in the given structures.

Q: 4. Which of the following acid-base reactions favor the products? A. HF + H₂O = F + H3O+ a b B. NH3…

Q: 2. List the six phases changes. Identify the exothermic changes and the endothermic ones. 3.…

A: As per bartleby guidelines I answered only first question so please don't mind thanks in advance.

Q: In naming alkyl halides, the -ide ending becomes -ic. If the halide is in an acidic form, the prefix…

Q: The mineral rhodochrosite [manganese(II) carbonate, MnCO3] is a commercially important source of…

A: We have to write the balanced half reaction for the oxidation of manganese in MnCO3 to MnO2

Q: When will combinations of chlorine (CI), bromine (Br), and iodine (1) not an oxidation number of -1?…

A: Answer:- Chlorine, bromine and iodine are halogens which have 7 electrons in their outermost shell.…

Q: What mass of SrCl₂ (d = 3.05 g/ma must you measure in air to obtain a true mass 3.4351 g ? Assume.…

A: •Given:- Density of SrCl2 (ρx) = 3.05 gm/ml True mass(Mx) = 3.4352 gm Density of air (ρn) = 0.0012…

Q: 2) What is the absorbance of a solution if the of of monochromatic light is 15.0 % ? transmittance

A: Given Transmittance (T) = 15% Absorbance (A) =?

Q: 6. Eggs shipped from a poultry farm in trucks. Each carton of eggs holds 12 eggs. The cartons of…

Q: 2. What is the molar mass of CaH₂NO₂?

A: Since each question is different from the other, we solve only first question according to the…

Q: What represents the oxidizing agent of an oxidation-reduction reaction? O one that donates electrons…

A: The oxidizing agent of oxidation-reduction reaction is one

Q: Which statement is correct? O Terpenes are not present in the plants Isopropyl group is the basic…

A: Terpenes are a class of natural products consisting of compounds with the formula (C5H8)n for n >…

Q: Allyl chloride is hydrolysed more readily than n-propyl chloride. Why?

A: CH2=CH-CH2-Cl CH3-CH2-CH2-Cl…

Q: Which numbered positions can the formal negative charge (on the top oxygen) be distributed to via…

A: Given : structure of molecule

Q: In the Periodic Table below, shade all the elements for which the neutral atom has a valence…

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

Q: In naming alkyl halides, the -ide ending becomes -ic. If the halide is in an acidic form, the prefix…

A: •Here given:- (Br-) . •This become acid so we have to write the name of this given halide and its…

Q: Draw the detailed mechanism of the synthesis of sertraline by arrow drag

Q: Draw all significant resonance structures for the following compound:

Q: A system releases 422 kJ of heat and does 203 kJ of work on the surroundings. What is the change in…

Q: We have learned that heat of combustion increases as we increase the number of carbons in a…

A: The structures of the given compounds are The compound with highest heat of combustion is

Q: The weak base methylamine, CH3NH2, is used in the production of insecticides and paint removers.…

A: CH3NH2 + H+ Br- → CH3NH3+Br- → CH3NH3Br here on the left side 1 atom of carbon is present and 6…

Q: Predict the products of the following reaction. If no reaction will occur, use the NO REACTION…

A: Answer:- This question is answered by using the simple concept of chemical reaction of metal…

Q: What is the molarity of ions in a 0.648 M solution of Ca(OH)₂ assuming the compound dissociates…

A: Given, Molarity of Ca(OH)2 solution = [Ca(OH)2] 0.648 M Ca(OH)2 completed dissociate in the…

Q: What is the correct order of flame atomic absorption spectroscopy (FAAS): Monochromator, lamp,…

A: Absorption spectroscopy is an analytical technique used to measure the concentration of a substance…

Q: The final major product of the following Edman reaction is CH3 NH₂ Ph Ph Ph ZH HO Ph—N=C Peptide HN…

A: we have to determine the product the given reaction

Q: Using only their location in the periodic table, rank the atoms in each set by decreasing atomic…

A: Given : (a) Mg, Be, Ba (b) Se, Br, Cl (c) Ca, Se, Ga we have to arrange the given atoms in order…

Q: Which of the following depicts constructive overlap of two orbitals in a pi-type interaction?

A: Given : diagram of overlapping

Q: to the true VS Precision is how close those accuracy values are to eacho 2. Suppose you are given a…

A: As you have requested for the solution of Q.3 we are providing you the solution for the same.…

Q: Fill in the blanks Complete the reaction map below by providing the answer for A-E. Write the IUPAC…

A: Organic reactions are chemical reactions involving organic compounds. Organic compounds are…

Q: The specific gravity of iron is 7.87 in the density of water at 4.00°C is 1.00 g/cm^3. You can use…

A: Specific gravity=(density of substance) ÷ (density of water @4° C) Given : density of water @ 4°C is…

Q: If a solution absorbs yellow light (in the range of 570 nm) what color will the solution appear to…

A: Since, In visible range of spectrum of light, if any color of light absorb then opposite of that…

Q: Balance the equation below using the oxidation number method. CH₂OH + MnO4- CO₂ + Mn²+ (in acidic…

A: Given that, CH3OH + MnO4- -------> CO2 + Mn+2 We have to balance this reaction using oxidation…

Q: For the following electron-transfer reaction: Hg2+ (aq) + 21 (aq) Hg(1) + I₂(s) The oxidation…

Q: The qualities/quantities of a gas are independent of one another. True 4 O False

A: •Given statement:- => The qualities/quantities of a gas are independent of one another.

Q: Of the bonds found in OH CH,—CH—CHCH,-0CH OH CH3 which is the most polar? OC-F O C-H OC-O OO-H

A: 1) we have to select the most polar bond 2) we have to find total number of carbon atoms in the…

Q: Provide the reagents needed to produce the compounds shown in each step in the spaces provided. OH…

Q: Weight out 17.02 grams of CaSO4. Add it to 250 mL of water in a 500 mL volumetric flask. Swirl to…

A: The mass of CaSO4, m = 17.02 g The volume of CaSO4, V= 500 mL = 0.500 L (1L = 1000 mL)

Concept explainers

Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

Question

Self-test 7B.3 As remarked in Self-test 7B.2, the normalized
wavefunction of the next higher energy level of the electron in this
model of the nanotube is (2/L)1/2 sin(2nx/L). What is the probability of
L/2?
finding the electron between x = L/4 and x =
Answer: 0.25

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Introduction and Principles 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

Would the light from fireflies be considered an example of a fluorescence or a phosphorescence process?
P7B.8 A normalized wavefunction for a particle confined between 0 and L in the x direction, and between 0 and L in the y direction (that is, to a square of side L) is y = (2/L) sin(Tx/ L) sin(Ty/L). The probability of finding the particle between x, and x, along x, and between y, and y, along y is P= "w°dxdy Calculate the probability that the particle is: (a) between x = 0 and x = L/2, y = O and y = L/2 (i.e. in the bottom left-hand quarter of the square); (b) between x = L/4 and x = 3L/4, y = L/4 and y = 3L/4 (i.e. a square of side L/2 centred on x = y = L/2).
(a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R and (b) compute linear density values for these same two directions for tungsten. (a) [110]: i [111]: i (b) [110]: i [111]: i atom/R atom/R 1/m 1/m
E7B.3(b) Which of the following functions can be normalized (in all cases the range for x is from x = -∞ to ∞, and a is a positive constant): (i) sin(ax); (ii) cos(ax) ex²? Which of these functions are acceptable as wavefunctions?
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
Calculate the energy separations in joules, kilojoules per mole, and electronvolts, and as a wavenumber, between the levels (a) n = 3 and n = 1, (b) n = 7 and n = 6 of an electron in a one-dimensional nanoparticle modelled by a box of length 1.5 nm.
Which of the following functions can be normalized (in all cases the range for x is from x= (-infinity) to (infinity), and a is a positive constant): (i) sin(ax); (ii) cos(ax)e-x^2? Which of these functions are acceptable as wavefunctions? Source: Atkins Physical Chemistry 11th Edition, E7B.4(b)
A two-level system is in a quantum state = α₁₁ + a22, which can be represented by the vector a = {a1, a2}. We are looking for the conditions under which is eigenstate of the operator c., defined below. 1) In the expression c.ỗ, c is a vector with components {Cr, Cy, Cz} ( C; are real numbers) and ỗ is a vector with components {σx, σy,σz} (σ¿ are 2 × 2 matrices). This means that the operator c. can also be represented by a 2 × 2 matrix. Write the matrix of the operator c. knowing that 0 0x = = (₁ }) = ( 5 ) . Oy σz= 0 (6-99) 1 0 1 0 2) In matrix form, the eigenvalue equation is AX AX, where A is the matrix of the operator of interest, X the column matrix representing the eigenvector and the corresponding eigenvalue. Write the eigenvalue equa- tion that needs to be verified for the quantum state to be an eigenvector of the operator c.. = 3) Note that AX = XX ⇒ (A - I)X 0, where I is the identity matrix. (AAI)X=0 is true if and only if det(A - I) = 0. Solve this equation for the operator…
P7E.1 If the vibration of a diatomic A-B is modelled using a harmonic oscillator, the vibrational frequency is given by w=(k; /u)", where u is the effective mass, µ=m,m,/(m, +m,). If atom A is substituted by an isotope (for example H substituted for 'H), then to a good approximation the force constant remains the same. Why? (Hint: Is there any change in the number of charged species?) (a) Show that when an isotopic substitution is made for atom A, such that its mass changes from m, to m, the vibrational frequency of A'-B, wAp can be expressed in terms of the vibrational frequency of A-B, @ An as o x=0 A (H/H", where u AB and u, are the effective masses of A-B and A'-B, respectively. (b) The vibrational frequency of 'HCl is 5.63 x 10"s". Calculate the vibrational frequency of (i) 'H*Cl and (ii) 'H"Cl. Use integer relative atomic masses. A'B
5. Determine yy for each of the following wavefunctions: (i =V-1) a) y (x) = e b) y(0) = sin 0 +i cose c) w(x) = A · e*.
P17.4 Show a. that (x) = 2 Â = x² - 0²/ax²; and ex²/2 is an eigenfunction of e b. that B(x) (where Â = x − a/ax) is another eigenfunc- tion of Â.
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 +