Calculating Spectroscopic Dissociation Energy for 127-I2 Molecule

[hellos]

Homework Statement

The spectroscopic dissociation energy of 127-I2 is 1.542eV. What wavelength of light would be needed to dissociate the molecule and have the atoms move apart at velocities of 1000 m/s?

Homework Equations

The Attempt at a Solution

What I did was convert 1.542eV to joules which became 2.47x10^-19 joules/mol. After that I found the total energy per bond by dividing the energy be avagadro's number = 4.1x10^-43. Then plugged it into wavelength = hc/E = 4.8x10^17m. But this didn't look right. Am I going about it the wrong way? Or should I just go straight to wavelength = hc/E using the 1.542eV to find the wavelength. Or work backwards using KE=1/2 mv^2?

Thanks in advance

 

[Borek]

1.542 eV is energy required for 1 molecule to be dissociated. However, your light must carry more energy, as the atoms need kinetic energy.

 

[Blueshift5]

I would approach this problem by first understanding the concept of spectroscopic dissociation energy and its relationship to the wavelength of light needed to dissociate a molecule. I would also make sure to have a clear understanding of the given information and any relevant equations.

To calculate the required wavelength of light, I would use the equation E=hc/λ, where E is the energy of the light, h is Planck's constant, c is the speed of light, and λ is the wavelength. In this case, we are given the energy (1.542eV) and we are trying to find the wavelength, so we can rearrange the equation to solve for λ.

λ = hc/E

Next, I would convert the given energy from electron volts (eV) to joules (J) to be consistent with the units in the equation. This can be done by using the conversion factor 1 eV = 1.602x10^-19 J.

λ = (6.626x10^-34 J*s * 2.998x10^8 m/s) / (1.542x10^-19 J)

Simplifying, we get:

λ = 4.08x10^-7 m

This is the wavelength of light needed to dissociate the 127-I2 molecule. However, the question also specifies that the atoms should move apart at velocities of 1000 m/s. This means that the light must also provide enough energy to give the atoms a kinetic energy of 1/2 mv^2 = 1/2 (2x127 amu) (1000 m/s)^2 = 1.27x10^-19 J.

Therefore, the total energy of the light should be the sum of the spectroscopic dissociation energy and the kinetic energy:

E_total = 1.542x10^-19 J + 1.27x10^-19 J = 2.812x10^-19 J

Using this value in the equation for wavelength, we get:

λ = (6.626x10^-34 J*s * 2.998x10^8 m/s) / (2.812x10^-19 J)

Simplifying, we get:

λ = 2.36x10^-7 m

This is the final answer for the required wavelength of light to dissociate the 127-I2 molecule and give the atoms a velocity of 1000

 

[Blueshift5]

I would first commend you for attempting to solve this problem using different methods. However, I would suggest that you approach the problem using the formula for calculating the wavelength of light needed to dissociate a molecule, which is λ = hc/DE, where λ is the wavelength of light, h is Planck's constant, c is the speed of light, and DE is the dissociation energy.

Using this formula, we can calculate the wavelength of light needed to dissociate 127-I2 with a dissociation energy of 1.542eV and atoms moving at 1000 m/s. First, we need to convert the dissociation energy into joules, which becomes 2.47x10^-19 J/mol. Then, we can plug in the values into the formula:

λ = (6.626x10^-34 J*s)(3.0x10^8 m/s)/(2.47x10^-19 J/mol) = 8.0x10^-8 m

Therefore, the wavelength of light needed to dissociate 127-I2 and have the atoms move apart at 1000 m/s is approximately 80 nanometers. This is within the ultraviolet range of the electromagnetic spectrum.

In conclusion, the correct approach to solving this problem is to use the formula for calculating the wavelength of light needed to dissociate a molecule, using the given dissociation energy and the desired velocity of the atoms.