Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 37, Problem 62P
(a)
To determine
The expression for
(b)
To determine
The separation
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The potential energy of a system of two atoms is given by the relation
U =-A/r + B/r10
A stable molecule is formed with the release of 8 eV energy when the interatomic distance is
2.8 Å. Find A and B and the force needed to dissociate this molecule into atoms and the
interatomic distance at which the dissociation occurs.
One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.
One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is
U(r) = Uo[(¹) ¹2 – ( )²]
where ro = 0.8 nm and U₁ = 6.1 eV.
Note: 1 eV = 1.6 × 10-19 J.
Some helpful units:
[Force] = eV/nm
[Energy] = eV
[distance] = nm
Equilibrium Distance
What is the distance between the atoms when the molecule is in stable equilibrium?
Click here for a hint
T'eq
Hint:
Hint:
Hint:
Hint:
Hint:
Hint:
Force
If the distance between the atoms increases from equilibrium by r₁ = 0.35 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract.)
Fr(req+r₁)
Hint:
Hint:
0.89105934nm
Kinetic Energy
Hint:
The atoms are oscillating back and forth. The maximum separation of the atoms is r₂ = 2 nm. What is the kinetic energy of the atoms when they are separated by the equilibrium distance?
Click here for a hint
K(req)
Hint:
Hint:
= -1.288eV/nm
3.99eV
Chapter 37 Solutions
Essential University Physics (3rd Edition)
Ch. 37.1 - Prob. 37.1GICh. 37.2 - If a scientist uses microwave technology to study...Ch. 37.3 - Prob. 37.3GICh. 37 - If you push two atoms together to form a molecule,...Ch. 37 - Prob. 2FTDCh. 37 - Prob. 3FTDCh. 37 - Does it make sense to distinguish individual NaCl...Ch. 37 - Prob. 5FTDCh. 37 - Prob. 6FTDCh. 37 - Radio astronomers have discovered many complex...
Ch. 37 - Prob. 8FTDCh. 37 - Prob. 9FTDCh. 37 - Prob. 10FTDCh. 37 - Prob. 11FTDCh. 37 - Prob. 12FTDCh. 37 - Prob. 13FTDCh. 37 - Prob. 14FTDCh. 37 - Prob. 15FTDCh. 37 - Prob. 16ECh. 37 - Prob. 17ECh. 37 - Prob. 18ECh. 37 - Prob. 19ECh. 37 - Prob. 20ECh. 37 - Prob. 21ECh. 37 - Prob. 22ECh. 37 - Prob. 23ECh. 37 - Prob. 24ECh. 37 - Prob. 25ECh. 37 - Prob. 26ECh. 37 - Prob. 27ECh. 37 - Prob. 28ECh. 37 - Prob. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33PCh. 37 - Prob. 34PCh. 37 - Prob. 35PCh. 37 - Prob. 36PCh. 37 - Prob. 37PCh. 37 - Prob. 38PCh. 37 - Prob. 39PCh. 37 - Prob. 40PCh. 37 - Prob. 41PCh. 37 - Prob. 42PCh. 37 - Prob. 43PCh. 37 - Prob. 44PCh. 37 - Prob. 45PCh. 37 - Prob. 46PCh. 37 - Prob. 47PCh. 37 - Prob. 48PCh. 37 - Prob. 49PCh. 37 - Prob. 50PCh. 37 - Prob. 51PCh. 37 - Prob. 52PCh. 37 - Prob. 53PCh. 37 - Prob. 54PCh. 37 - Prob. 55PCh. 37 - The transition from the ground state to the first...Ch. 37 - Prob. 57PCh. 37 - Prob. 58PCh. 37 - Youre troubled that Example 37.1 neglects the mass...Ch. 37 - Prob. 60PCh. 37 - The Madelung constant (Section 37.3) is...Ch. 37 - Prob. 62PCh. 37 - Prob. 63PCh. 37 - Prob. 64PCh. 37 - Prob. 65PCh. 37 - Prob. 66PCh. 37 - Prob. 67PCh. 37 - Prob. 68PPCh. 37 - Prob. 69PPCh. 37 - Prob. 70PPCh. 37 - Prob. 71PP
Knowledge Booster
Similar questions
- In a Si semiconductor sample of 200 am length at 600 K the hole concentration as a' function of the sample length follows a quadratic relation of the form p (x) = 1 x1015x, at equilibrium the value of the electric field at 160 jum will be: O 1.935 V/cm O 3.250 V/cm O 5805 V/cm O 55.56 V/cm O 6.450 V/cmarrow_forwardGraph below shows the electron occupancy probability P(E) as a function of energy for Bismuth (mBi = 3.47 × 10-25 kg) at the temperature T = 0 K. What is the number of conduction electrons per unit volume for Bismuth? 1 1 2 3 4 5 6 7 8 E (ev) P(E)arrow_forwardThe potential energy of one of the atoms in the hydrogen molecule is given by U(x) = U₁ (e-2(1-10)/b - 2e-(1-10)/b) where U₁ = 2.36 [eV], zo = 0.037 [nm], and b = 0.034 [nm]. Note that 1 [eV] = 1.6 × 10-¹⁹ [J]. Part (a) Find the energy of the hydrogen molecule in ground state. Part (b) If the measured energy of each atom in the hydrogen molecule is E= -1.15 [eV], where are the classical turning points of the atomic vibration in the hydrogen molecule?arrow_forward
- gc (E) = (m*n/π2*ћ3 )*sqrt(2m*n (E-Ec)) Note: Dimension of gc (E) = 1/m3*J Effective mass = m*n Use the Density of states of the conduction band gc(E) to evaluate the number of states/cm3in the conduction band at temperature T in the energy range Ec to Ec+kT, as you evaluate the integral, assume that the effective mass is independent of the energy and can be treated as a constant.arrow_forwardThe frequency of vibration of the H2 molecule is 1.32*1014 Hz. (a) find the relative populations of the v=0,1,2,3 and 4 vibrational states at 5000K (b) can the populations of the v=2 and v=3 states ever be equal? if so, at what temperature does this occur.arrow_forwardA brittle material has the properties Sut=30 kpsi and Suc=90 kpsi. Using the brittle Coulomb- Mohr and modified-Mohr theories, determine the factor of safety for the following states of plane stress. Ox=-15 kpsi, o,=10 kpsi, txy=-15 kpsiarrow_forward
- 6c.2. The integrate the electron density n is the integral of the density state using the 2D density of states and the Fermi-Dirac distribution, EF = [ƒ¥D(E) · 9(E) de · n = Fermi - Dirac distribution density of state in 2D per unit area → fFD(E): = g²D (E) 1 eß(ε-μ) + 1 1 dN (2D) A dE To show that the chemical potential of a Fermi gas in two dimensions is, H(T) = k¸T \n [exp (™ 47 In [exp (m²) - 1] mkgT || mº πηarrow_forwardA gas of identical diatomic molecules absorbs electromagnetic radiation over a wide range of frequencies. Molecule 1, initially in the υ = 0 vibrational state, makes a transition to the υ = 1 state. Molecule 2, initially in the υ = 2 state, makes a transition to the υ = 3 state. What is the ratio of the frequency of the photon that excited molecule 2 to that of the photon that excited molecule 1? (a) 1 (b) 2 (c) 3 (d) 4 (e) impossible to determinearrow_forwardView a system of two particles that do not interact with each other, where each particle can occupy three possible states, each with energy &, 2ɛ, 3E (i) Marwell-Boltzmann: Na. Configuration 1 2 3 4 S 6 7 2 9 Nader Conligation 1 2 2 + 1 2 5 6 (1) Fermi-Dirac 3 No. Configuration E AG A A B B AA A A Distinguishable 28 E AB (6) Boson: Base- Ginstein: Indistinguishable င် A A B A A 8 28 AA A A 38 A 2 A AB B A CO B A JE AA A A Energy system A A wwwww Indistinguishable We know formion follow exclusion principle. 28 38 Smarty tem 28 32 38 4E SE SE Energy system 22 48 68 38 48 SE 38 4€ SE Calculate the average energy of the system as a temperature function for the three statistics above.arrow_forward
- a) Starting from a general fornula of desity of States. g(k) dk= Vkdk 272 Show that g(w) dw= 3x Vw°dw for Phonons under the assumption thait the phonoh dre aicoustic, meaning U = does not depend 3. on W or k. 3N b) In a solid of N atoms, there are vibrational modes(phonons) with the highat frequercy Wp.arrow_forwardCu Assume that the crystal structure of metallic copper (Cu) results in a density of atoms p = 8.46 × 10²m 3. Each Cu atom in the crystal donates one electron to the conduction band, which leads, for the 3-D Fermi gas, to a densityu of states g(ɛ) = 2 x = ( 2 m ² ) ² 1/2 where m is the effective mass of the conduction electrons. In the low temperature limit (i.c. T = 0 K), find the Fermi energy E, in units of eV. You may assume m* to be equal to the free electron mass marrow_forwardEstimate kBT at room temperature, and convert this energy into electronvolts (eV). Using this result, answer the following: (a) Would you expect hydrogen atoms to be ionized at room temperature? (The binding energy of an electron in a hydrogen atom is 13.6 eV.) (b) Would you expect the rotational energy levels of diatomic molecules to be excited at room temperature? (It costs about 10−4 eV to promote such a system to an excited rotational energy level.)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning