Using the Boltzmann’s law, show that, for a spin-1/2 nucleus at thermal equilibrium at temperature T in a magnetic field Bo, the probabilities of finding it in the a and ß states are: yhBo e kT ; Pg 1 Pa yhBo 1+e kT yhBo 1+e kT

Using the Boltzmann’s law, show that, for a spin-1/2 nucleus at thermal equilibrium at temperature T in a magnetic field Bo, the probabilities of finding it in the a and ß states are: yhBo e kT ; Pg 1 Pa yhBo 1+e kT yhBo 1+e kT

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter20: Molecular Spectroscopy And Photochemistry

Section: Chapter Questions

Problem 56AP

See similar textbooks

Related questions

Q: Molecular Geometry: The VSEPR Model Table 2: Molecular Models Molecule Sketch of Lewis Dot Structure...

A: In the Lewis dot structure we consider the lone pairs of each atoms where as in shape determination ...

Q: At 298.15K Ihe osmotic pressure of the unknown substance was found to be at 2.25x10 Pa. If the conce...

A: Temperature = 298.15 K Osmotic pressure of solution = 2.25 x 104 Pa Concentration of solution = 12.7...

Q: Suppose you dissolve silver chloride (AgCI), a weak electrolyte, in water. Indicate the effect on th...

A: These type of questions are based on the common ion and odd ion effect. Let us understand it in deta...

Q: Question 2 Rank the following carbon atoms in the order of increasing deshielding. HO: A C Most desh...

A: Different signals obtained in 1HNMR are due to different chemical shift (ppm) for respective proton....

Q: 2) ОN- -CH,CI CH,COONA CH3COОH sol.

A: Electron withdrawing substituents destabilize the carbocation that's why SN1 reaction tendency decre...

Q: Consider the following reaction: NH4HS(s)=NH3(g)+H2S(g)NH4HS(s)=NH3(g)+H2S(g) An equilibrium mixture...

A: At equilibrium, the rate of the forward and the reverse reaction is the same and the concentration o...

Q: n2+2o2= n2o4. if 15.0g of N2O4 was produced, how many moles of o2 were required

Q: An aqueous solution of hydrofluric acid is 30.0% HF, by mass, and has a density of 1.101 g/mL. What ...

A: X% of a compound by mass means that there is X g of that compound present in a solution of total mas...

Q: For the dehydration shown, use curved arrows to show the formation of the carbocation intermediate i...

A: Alcohol in presence of H2SO4 undergoes elimination reaction. The more substituted alkene will be the...

Q: Provide suitable IUPAC name for each of the following compounds.

Q: Given: Enthalpy of atomisation of calcium =+ 178 kJ First ionisation energy of calcium =+590 kJ Seco...

Q: Provide suitable IUPAC name for each of the following compounds.

Q: Consider the following reaction: NH4HS(s)=NH3(g)+H2S(g)NH4HS(s)=NH3(g)+H2S(g) An equilibrium mixture...

Q: a) Please provide the reaction mechanism for both of the following reactions

A: bromo benzene should product using this reaction mechanism should given

Q: A 600.0 mg sample consisting of only CaC2O4and Mg C2O4is heated at 500oC converting the two salts to...

A: A question based on mole concept that is to be accomplished.

Q: Thermosetting polymers chemically changed at high .temperatures True O False O Electrons spin around...

A: About thermosetting polymers:

Q: 4. An aqueous solution of AgCl wherein u-D0.10 Ksp of AGCI Ksp' of AGCI

A: 4. Solution - According to the question - Given - the solubility of AgCl decreases because NaCl is a...

Q: A. What are the commons causes of fire at home? (at least 2) 1. Materials should explain its physica...

Q: What is the minimum mass of Mg(NO3)2 that must be added to 1.00L of a 0.760 M HF solution to begin p...

A: Let us solve this question step by step.

Q: B. For water with the ionic characteristic defined by the analysis given below identify the major sa...

A: A question based on mole concept that is to be accomplished.

Q: The table below shows the standard enthalpy of formation of carbon dioxide, water and nitromethane, ...

A: Combustion of CH3NO 4CH3NO(l) + 5O2(g) ------> 4CO2(g) + 6H2O(l) + 2N2(g) ∆Hf (...

Q: Give the organic reactant needed to complete each of the following Grignard reactions. Write out the...

A: Grignard reagent, any of numerous organic derivatives of magnesium (Mg) commonly represented by the ...

Q: Reactions Mechanism Major Product Mechanism Minor Product (SN1, SN1, E1, E2) (SN1, SN1, E1, E2) t-BU...

A: E2 and SN2 are the conjugate reaction and there is always a race between E2 and SN2 . In presence of...

Q: Time Altitude Pressure Temperature Volume Moles 9:00 pm 40 km 9.54 x 10 atm 115,580 L 9:10 pm 20 km ...

Q: SH-CH, Br (CH,),C- CH- CH, Br CH,

A: E1 elimination is a order reaction and let us discuss its mechanism,

Q: Reactions Mechanism Major Product Mechanism Minor Product (SN1, SN1, E1, E2) (SN1, SN1, E1, E2) t-BU...

A: Predict the suitable mechanism for the following reactions.,

Q: Provide suitable IUPAC name for each of the following compounds

Q: Calculate the pH of a 0.256 M solution of ethylenediamine (H,NCH,CH,NH, ). The pK, values for the ac...

Q: For a solution in which u = 8.0 x 10, calculate K, for Pbl,. The thermodynamic constant of the solub...

Q: A solution is prepared by mixing 290 mL of 0.700 M NH3 and 170 mL of 0.700 M HCI. Assuming that the ...

Q: a) BRCH2CH2B1 + NaSCH2CH;SNa C4H&S2 ↑

Q: Given the reaction: CO2(g) + H2(g) ⇌ H2O(g) + CO(g) If Kc = 1.6 at 1263 K, calculate the number of m...

Q: Density of an aqueous solution of nitric acid is 1.43 g/mL. If this solutioin contained 36.0% nitric...

A: Given, Density of an aqueous solution of nitric acid = 1.43 g/mL Mass % of nitric acid = 36.0 % Volu...

Q: A 500 m2 botanical garden which harvest 1000 flowers per day of 15 variations, in a year the average...

A: You have posted multipart of question as per the guidelines i have solved first three subparts kindl...

Q: The equilibrium for the various proportions of the amyl ester of dichloroacetic acid (CHCI, COOC,H) ...

A: The solution of the question is given below:

Q: In the above redox reaction, use oxidation numbers to identify the element oxidized, the element red...

A: Identify the oxidized and reduced element or ion--

Q: a) Briefly describe the meaning of chromophores. b) (i) Depict the graph using Microsoft excel (ii) ...

A: (a) Chromophore is a group which exhibit absorption of electromagnetic radiation in UV or Visible re...

Q: Reactions Mechanium Majar Product Mechanism Minar Product (S1, , EL, E2) (, Sd, , 2) (S)2-Bromooctan...

Q: A 10µg/ml solution is prepared by diluting. ul of a 10mg/ml solution into 1ml of water.

A: Here we are diluting the concentrated sample to get a diluted sample.

Q: II. TABLE COMPLETION: Complete the table below by supplying the correct answer. ELEMENT PERIOD ORBIT...

Q: Calculate the heat evolved when 13.56g of oxygen gas (O2) is used to burn white phosphorus at stand...

A: 1) Given, P4(s) + 5O2(g) ➝ P4O10(s) ∆H = -3013 kJ/mol ∆H is in negative (-) which indicate release...

Q: Predict the FINAL product for the following synthetic transformation: NH2 HNO, H2SO, NH2 NH2 NH2 O,N...

Q: classify whether it is greater than, less than, or equal

A: Since you have posted multiple questions, the answer for first question is given below. Kindly repos...

Q: Write the chemical reaction between Brady’s reagent and acetaldehyde, benzaldehyde and propanone

A: Brady's reagent react with carbonyl compounds to form colored precipitate.

Q: Balance the decomposition reaction: Hypothesis: What percentage do you predict for the KCI (potassiu...

A: Balanced equation for the decomposition of KClO3 2KClO3 (s) → 2KCl (s) + 3O2 (g)...

Q: Explain how you would synthesize the following organic molecule. Be sure to list the name of the org...

Q: What is the best choice of reagent(s) to perform the following transformation? ?

A: The conversion of alkene into an alkane involves the reduction( addition of hydrogens).

Q: A 15% milk solution is prepared by dissolving g of milk in 0.5L of water.

Q: What is the pH of a 0.1250 M CH3NH3Br? Kb for CH3NH2 is 3.70e-4.

A: Given, The pH of a 0.1250 M CH3NH3Br is : Kb for CH3NH2 is 3.70e-4.

Q: A chemist measures the enthalpy change AH during the following reaction: 2 Na(s) + Cl,(9)→2 NaCl(s) ...

A: Given- 2Na+Cl2->2NaCl. ∆H=-822KJ

Question

Using the Boltzmann’s law, show that, for a spin-1/2 nucleus at thermal
equilibrium at temperature T in a magnetic field Bo, the probabilities of finding it in the a and ß states
are:
yħBo
e kT
1
yhBo
1+е kт
Pa
; Pg :
yhBo
1+е kT

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

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

Why is 133C-133C spin-spin splitting not observed in ordinary organic compounds?
Calculate the ratio of nuclei in the higher spin state to those in the lower spin state, Nh/Nl, for 1H at 25°C in an applied field strength of 7.05 T.
(b) A system with chemical potential u = 12.5 meV contains identical particles each with integer spin and has a single quantum state at energy E, = 0 meV. The temperature of the system is fixed at 290 K. To three significant figures, what is the ratio Pg/P1, where P is the probability of finding a single particle in the state Eo, and P3 is the probability of finding 3 particles in this state? P3/P (Input your answer as a number.)
For a 1H nucleus (a proton), what are the magnitude of the spin angular momentum and what are its allowed components along the z-axis? Express your answer in multiples of ħ. What angles does the angular momentum make with the z-axis?
How can i calculate value of nuclear spin(I)? Why 11B’s I is 3/2 ?
Imagine a system in local thermal equilibrium at temperature T which contains both massless spin-1/2 particles (Weyl fermions) and massless spin-1 particles, both with vanishing chemical potential. For which particle species will the contribution to the energy density be larger? (a) Spin-1/2 particles (b) Spin-1 particles (c) They will be equal (d) Not enough information
The nuclear spin of deuterium, D, is I= 1. Calculatethe ratio of the number of ways of achieving rotational statesw ith odd and even values of J.
Find the ratio of the populations of the two spin states of protons in a magnetic field of 4.6973 T at 25°C. gp = 5.5857 UN = 5.0508 x 10-27 J/T
What is the resonance frequency of a proton in a magnetic field of 14.1 T?
P21.6 The operator for the square of the total spin of two electrons is Stotal = (S₁ + S₂)² = S² + S² + 2(S1xS2x + S1yS2y + $1$22). Given that iħ S₁α = /B₁ S₁,α = 22²1 2 SxB = ħ 2 α, B, S₂α = = 九↓2 ħ α, iħ ħ S,ß α₁ S₂B = 1/- B₁ a, 2 2 show that a (1) a (2) and ß (1) ß (2) are eigenfunctions of the operator Stotal. What is the eigenvalue in each case?
Consider a one-dimensional spin 1 model, defined by the Hamiltonian N N H = -JES;Si+1+DES}, where J> 0, D > 0 and Si = -1, 0, 1 (a) Use of periodic conditions of contour, calculate the automatic values of the transfer matrix. (b) Calculate the internal energy and entropy per spin. (c) What is the ground state (T = 0) of this model as a function of the parameter d = DIJ www Get an asymptotic form of the eigenvalues of the download matrix, t → 0 in the d-axis regions
2. A combined system is formed from two separate systems of N localized atoms of spin-1/2 each. While the two systems remain separate (a) Find the number of configurations which give a total spin excess S = S, +S, where S, and S, are the excess spins of the separate systems. (b) For what values of S, and S, is this number of configurations maximum?