Consider a diatomic molecule with a reduced mass of 30.0000 amu with a ground st

Question

Consider a diatomic molecule with a reduced mass of 30.0000 amu with a ground state electronic potential well described with a Morse function with a dissociation energy of 2.00000 eV, and equilibrium bond length of 2.00000 Ångstroms, and a harmonic vibrational frequency of 200.00 cm-1. Calculate the following requested quantities to six significant figures.

a) What is the amount of energy (in eV) required to stretch the bond of this molecule from 2.00000 to 4.00000 Ångstroms?

b) What is the zero-point energy of this molecule (in cm-1)?

c) What is the frequency (in cm-1) of the R(0) line of the IR fundamental band of this molecule?

d) What is the frequency (in cm-1) of the P(20) line of the IR second overtone band (v'=3v”=0) of this molecule?

e) What is the frequency (in cm-1) of the R(20) line of the IR first hot band fundamental (v'=2v”=1) of this molecule?

Explanation / Answer

Answer:

a) by law of diatomic molecule stretching the bond of this molecule from 2.00000 to 4.00000 Ångstroms required is (2)4 ie 16eV

b) zero-point energy of this molecule (in cm-1) 0

c) frequency (in cm-1) of the R(0) line of the IR fundamental band of this molecule v=1/2pi under root(e/m) which comes out to be 1

d) frequency (in cm-1) of the P(20) line of the IR second overtone band (v'=3v”=0) of this molecule v=1/2pi under root(e/m) which comes out to be 0

e) frequency (in cm-1) of the R(20) line of the IR first hot band fundamental (v'=2v”=1) of this molecule v=1/2pi under root(e/m) which comes out to be 0

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.