Problem 18.23 The force constant for a 1H127I molecule is 325 Nm1. Part A Calcul

Question

Problem 18.23

The force constant for a 1H127I molecule is 325 Nm1.

Part A

Calculate the zero point vibrational energy for this molecule for a harmonic potential.

Express your answer with the appropriate units.

SubmitMy AnswersGive Up

Part B

Calculate the light frequency needed to excite this molecule from the ground state to the first excited state.

Express your answer with the appropriate units.

Problem 18.23

The force constant for a 1H127I molecule is 325 Nm1.

Part A

Calculate the zero point vibrational energy for this molecule for a harmonic potential.

Express your answer with the appropriate units.

SubmitMy AnswersGive Up

Part B

Calculate the light frequency needed to excite this molecule from the ground state to the first excited state.

Express your answer with the appropriate units.

Explanation / Answer

Part A. calculate reduced mass for the molecule

reduced mass, m = M1.M2/M1+M2

M1 and M2 are in kg

M1 = 1/6.022 x 10^26 = 1.6606 x 10^-27 kg

M2 = 27/6.022 x 10^26 = 4.4836 x 10^-26 kg

= 1.6606 x 10^-27 x 4.4836 x 10^-26/1.6606 x 10^-27 + 4.4836 x 10^-26

= 1.6013 x 10^-27 kg

Vibrational frequency for HI = sq.rt.(force constant/reduced mass)

= 1/2pi.sq.rt.(325/1.6013 x 10^-27)

= 7.17 x 10^17 s-1

Now, zero point vibrational energy E would be,

E = hv/2

   = 6.626 x 10^-34 x 7.17 x 10^17/2

   = 2.37 x 10^-16 J

Part B. For excitation from ground state n = 1 to excited state n 2

we have,

deltaE = hc/lambda = 2.18 x 10^-18[1-1/4] = 1.635 x 10^-18 J

E = hv = 1.635 x 10^-18

light frequency needed for excitation

= 1.635 x 10^-18/6.626 x 10^-34 = 2.47 x 10^15 s-1

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects