Calculating Energy Increase of Br2(ground) to 2Br(ground)

[gazepdapi1]

This is the problem:
The limit of continuous absorption for Br2 gas occurs at 19750cm^-1. The dissociation energy that occurs is:

Br2(gorund) = Br(ground) + Br(excited)

The transition of ground bromine atom to an excited one corresponds to a wave number of 3685 cm^-1:

Br(ground) = Br(excited)

Calculate the energy increase for the process in cm^-1 and eV:
Br2(ground) = 2Br(ground)

I think I need to use: v(limit) = D'0 + v0 = D0 +v(atomic)

What I have so far is:
Br2(ground) = Br2(exited) = 19750-3685 = 16065 cm^-1
So, D'0 = 16065cm^-1. Then Br2(ground) = 2(16065) = 32130 cm^-1

Can someone check if I have this correct? This Hw is due in like 2 hours.
Thanks.

 

[Jhero]

Hello!

It looks like you are on the right track with your calculations. Here is a breakdown of the steps you took and some additional information that may help you:

1. The limit of continuous absorption for Br2 gas occurs at 19750 cm^-1. This means that at this frequency, all the available energy levels for Br2 have been filled and further absorption is not possible.

2. The dissociation energy for Br2 is the energy required to break the bond between the two bromine atoms. This occurs at 19750 cm^-1.

3. The transition from ground state Br2 to excited state Br corresponds to a wave number of 3685 cm^-1. This means that the energy difference between the two states is 3685 cm^-1.

4. Using the equation v(limit) = D'0 + v0, we can rearrange it to solve for D'0, the dissociation energy: D'0 = v(limit) - v0. Plugging in the values, we get D'0 = 19750 cm^-1 - 3685 cm^-1 = 16065 cm^-1.

5. Since each bromine atom contributes half of the energy in Br2, we can divide D'0 by 2 to get the dissociation energy for each bromine atom. This gives us 16065 cm^-1 / 2 = 8032.5 cm^-1.

6. To convert to eV, we use the conversion factor 1 cm^-1 = 1.23984 x 10^-4 eV. Multiplying the dissociation energy by this factor, we get 8032.5 cm^-1 x 1.23984 x 10^-4 eV = 0.996 eV.

So, the energy increase for the process is 3685 cm^-1 or 0.996 eV. This means that when a ground state Br2 molecule absorbs a photon with a frequency of 3685 cm^-1, it gains enough energy to break the bond between the two bromine atoms and create two excited state Br atoms.

I hope this helps and good luck with your homework!