The Morse potential is given by the following expression: V (x) = ED · (1 −...
The Morse potential is given by the following expression: V (x) = ED · (1 − e -ax)2
a.) At what value for x is V(x) a minimum? (First derivative might be helpful.)
b.) What is V(x) when x → ∞ ?
c.) What is V(x) when x → 0 ?
d.) What is the difference between ED and a measured dissociation energy
Homework Answers
Add Answer to:
The Morse potential is given by the following expression: V (x)
= ED · (1 −...
Draw a typical Morse potential energy surface for a diatomic molecule. Label the following i) The...
Draw a typical Morse potential energy surface for a diatomic molecule. Label the following i) The vertical and horizontal axes ii The equilibrium bond length. iii) The v=0, 1, 2 vibrational iv) The dissociation energy (Do) from the v-0 vibrational level 1 levels.
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The...
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic oscillator model, but much more accurately by including a small anharmonic correction term: En/hcVe(n 1/2) - vexe(n + 1/2)2. From fits to experimental data, the values of the constants are 325.32 cm and exe 1.08 cm .5 10 15 (a) Calculate the...
2.2) The Morse interatomic potential for a diatomic molecule is given by VM(r) D[1-e-a-1 r-ro where...
2.2) The Morse interatomic potential for a diatomic molecule is given by VM(r) D[1-e-a-1 r-ro where r is the interatomic distance. a) Sketch the potential, and indicate its attractive and repulsive region. [4 marks] b) Show that the equilibrium bond length is given by r ro. [4 marks] c) Determine the dissociation energy of the diatomic molecule. [4 marks]
For a particle of mass m, consider a Morse potential of V. V(x) cosh (Bx)' where...
For a particle of mass m, consider a Morse potential of V. V(x) cosh (Bx)' where V> 0 and 8 >0. (a) Illustrate this potential graphically as a function of x. (b) Write the WKB quantization condition: of pladě = (n+ + ) 7, n=0,1,2,3,,.... in terms of the bound state energies En and V(x). What are I'min and Imax in this case, and what is the physical meaning/interpretation of Imin and Imax ? (C) Use WKB methods to determine...
a) Find the potential V(x) associated with the wavefunction ψ(x) = Csech(ax) given that its energy...
a) Find the potential V(x) associated with the wavefunction ψ(x) = Csech(ax) given that its energy eigenvalue is zero (i.e. E = 0). b) Plot V(x) and ψ(x) on the same graph.
A particle subject to a potential V (x) has the form 1/ cosh(kx). Obtain an expression for V (x) and the value of the corresponding energy level.
A particle subject to a potential V (x) has the form 1/ cosh(kx). Obtain an expression for V (x) and the value of the corresponding energy level.
I know how to do A but not sure how to do B, C and D....
I know how to do A but not sure how to do B, C and D.
Thank you so much!
5. Vibration of diatomic molecule (20 points total) The adjacent figure shows the experimentally detemined potential energy curve of the electronic ground state of Br2 with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic-oscillator model but much more accurately by including a small anharmonic correction term: En/hc = e(n +1/2) - exe(n...
zone 1 Consider the following piecewise continuous, finite potential energy: ro; x < -a V(x)={-U, ;...
zone 1 Consider the following piecewise continuous, finite potential energy: ro; x < -a V(x)={-U, ; -a sxs a zone II U, > 0 (+ve) 10 ; x> a We consider zone III E>0: Unbound or scattering states (a) State the Time independent Schrödinger's Equation (TISE) and the expression of wave number k in each zone for the case of unbound state (b) Determine the expression of wave function u in each zone. (e) Determine the expression of probability Density...
5. (10 points) A simple function that looks like the potential well of a diatomic molecule...
5. (10 points) A simple function that looks like the potential well of a diatomic molecule is the Morse potential given by: U(x) = D. (1-e-Bx) (1) where, x is the displacement of the bond from its equilibrium position, and D. is the value of U(x) at large separations. D. is called the classical dissociation energy and is characterized by the depth of the potential well. We can expand U(x) in a Taylor series about x = 0 to obtain...
2) For the given equations: V(z) = { é o se} V(,0) = V $(x) +...
2) For the given equations: V(z) = { é o se} V(,0) = V $(x) + V1() + vee(r) a) Write the expression for 4A (x,t). b) What is the expectation value for (E) ? Write the expression in E.. c) Write the expression for W.(x,t) at E2 for t>t, and what is the probabilities at t2 > ti d) Write the another expression for WB(x, 0) with the same value of (E). e) Write the another expression for c(x,0)...
Draw a typical Morse potential energy surface for a diatomic molecule. Label the following i) The vertical and horizontal axes ii The equilibrium bond length. iii) The v=0, 1, 2 vibrational iv) The dissociation energy (Do) from the v-0 vibrational level 1 levels.
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic oscillator model, but much more accurately by including a small anharmonic correction term: En/hcVe(n 1/2) - vexe(n + 1/2)2. From fits to experimental data, the values of the constants are 325.32 cm and exe 1.08 cm .5 10 15 (a) Calculate the...
2.2) The Morse interatomic potential for a diatomic molecule is given by VM(r) D[1-e-a-1 r-ro where r is the interatomic distance. a) Sketch the potential, and indicate its attractive and repulsive region. [4 marks] b) Show that the equilibrium bond length is given by r ro. [4 marks] c) Determine the dissociation energy of the diatomic molecule. [4 marks]
For a particle of mass m, consider a Morse potential of V. V(x) cosh (Bx)' where V> 0 and 8 >0. (a) Illustrate this potential graphically as a function of x. (b) Write the WKB quantization condition: of pladě = (n+ + ) 7, n=0,1,2,3,,.... in terms of the bound state energies En and V(x). What are I'min and Imax in this case, and what is the physical meaning/interpretation of Imin and Imax ? (C) Use WKB methods to determine...
I know how to do A but not sure how to do B, C and D.
Thank you so much!
5. Vibration of diatomic molecule (20 points total) The adjacent figure shows the experimentally detemined potential energy curve of the electronic ground state of Br2 with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic-oscillator model but much more accurately by including a small anharmonic correction term: En/hc = e(n +1/2) - exe(n...
zone 1 Consider the following piecewise continuous, finite potential energy: ro; x < -a V(x)={-U, ; -a sxs a zone II U, > 0 (+ve) 10 ; x> a We consider zone III E>0: Unbound or scattering states (a) State the Time independent Schrödinger's Equation (TISE) and the expression of wave number k in each zone for the case of unbound state (b) Determine the expression of wave function u in each zone. (e) Determine the expression of probability Density...
5. (10 points) A simple function that looks like the potential well of a diatomic molecule is the Morse potential given by: U(x) = D. (1-e-Bx) (1) where, x is the displacement of the bond from its equilibrium position, and D. is the value of U(x) at large separations. D. is called the classical dissociation energy and is characterized by the depth of the potential well. We can expand U(x) in a Taylor series about x = 0 to obtain...
2) For the given equations: V(z) = { é o se} V(,0) = V $(x) + V1() + vee(r) a) Write the expression for 4A (x,t). b) What is the expectation value for (E) ? Write the expression in E.. c) Write the expression for W.(x,t) at E2 for t>t, and what is the probabilities at t2 > ti d) Write the another expression for WB(x, 0) with the same value of (E). e) Write the another expression for c(x,0)...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago