The energy of a vibrating molecule is quantized much like the energy of an electron...

Agaiepsh

Agaiepsh

Answered

2021-11-15

The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation: En=(n+12hv) where n is a quantum number with possible values of 1, 2, ... and v is the frequency of vibration. The vibration frequency of HCI is 8.85×1013s1 What minimum energy is required to excite a vibration in HCl? What wavelength of light is required to excite this vibration?

Answer & Explanation

Linda Tincher

Linda Tincher

Expert

2021-11-16Added 14 answers

Step 1
A vibrating molecule's energy is En=(n+12)hv when the quantum number is n; h=6.626×1034js and v is the vibration frequency.
Given that the vibration frequency of HCl is 8.85×1013s
Find the wavelength of light that can trigger this vibration and the minimal energy needed to cause HCl to vibrate.
Solution: The difference between the energies of the two lowest quantum numbers should represent the minimal energy needed to cause HCl to vibrate. Use E=hcλ to find the vibration's corresponding wavelength where c=3.00×108ms
Step 2
Since n should be a positive number in a quantum system, the transition that corresponds to the minimal amount of energy needed to for HCl to vibrate is n=1n=2. Calculate E1  and  E2
E1=(n+12)hv=(1+12)6.626×1034js8.85×1013s=8.796015×1020j
E2=(n+12)hv=(2+12)6.626×1034js8.85×1013s=1.466×1019j
Step 3
Calculate
E12=EfEi
E12=E2E1=1.466×1019j8.796×1020j=5.864×1020J
Step 4
Calculate λ using E=hcλ
λ12(6.626×1034Js)(3.00×108m/s)5.864×1020J=3.3898×106m1×109nm1m=3390nm
E12=5.864×1020j
λ12=3390nm

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?