Experimentally the ionization energy of hydrogen is 1312.2 kJ / mol. What would be the wavelength (nm) of a photon with enough energy to ionize one atom of hydrogen?
They give the equation E=hcR but those are all known constant values and none include mols so I'm very confused.
Thanks!
divide the energy by 2*avagrado's number, the number of atoms in a mole of H2
Then, use Planck's equation to find the wavelength.
Wait, what's planck's equation??
Energy= Planck's constant* speedlight/wavelength
Ok that's what I thought!
So my answer should be 182.45 nm, yes?
Because I had to convert kJ to J
So I did:
1312200/2(6.022x10^23)
6.626x10^-34(3x10^8)/ans
and then that answerx 10^9 to convert to nm
Where did I go wrong because that answer wasn't correct =(
Here is a site that may be interesting to you and may shed some light on your problem.
http://en.wikipedia.org/wiki/Molar_ionization_energies_of_the_elements
This shows ionization energy = 1312 kJ/mol H ATOMS.
To determine the wavelength of a photon with enough energy to ionize one atom of hydrogen, you can use the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength.
First, let's convert the given ionization energy from kJ/mol to J/atom. Since there are Avogadro's number (6.022 × 10^23) of atoms in one mole, we can divide the ionization energy by Avogadro's number to get the energy per atom.
1312.2 kJ/mol = (1312.2 × 10^3 J/mol) ÷ (6.022 × 10^23 atoms/mol) ≈ 2.182 × 10^-18 J/atom
Now, we can substitute this energy value into the equation to find the wavelength (λ).
2.182 × 10^-18 J/atom = (6.626 × 10^-34 J·s) × (2.998 × 10^8 m/s) ÷ λ
Rearranging the equation and solving for λ:
λ = (6.626 × 10^-34 J·s) × (2.998 × 10^8 m/s) ÷ (2.182 × 10^-18 J/atom)
Calculating this expression:
λ ≈ 9.104 × 10^-8 m
Finally, to convert the wavelength from meters (m) to nanometers (nm), we multiply by 10^9:
λ ≈ 9.104 × 10^-8 m × 10^9 nm/m ≈ 91.04 nm
Therefore, the wavelength of a photon with enough energy to ionize one atom of hydrogen is approximately 91.04 nm.