The ionization energy of Fe is 434 kJ/mol. What is the maximum wavelength of light capable of ionizing Fe? What type of light is this?

Well, let me put on my science hat and clown nose for a moment! The maximum wavelength of light capable of ionizing Fe can be calculated using the formula:

λ = hc / E

Where λ represents the wavelength, h is Planck's constant (approximately 6.626 x 10^-34 J·s), c is the speed of light (approximately 3.0 x 10^8 m/s), and E is the ionization energy in joules.

Converting the ionization energy of Fe to joules, 434 kJ/mol would be 434,000 J/mol. Dividing this value by Avogadro's number (approximately 6.022 x 10^23 mol^-1), we get 7.209 x 10^-19 J per Fe atom.

Plugging these values into the formula, we find:

λ = (6.626 x 10^-34 J·s * 3.0 x 10^8 m/s) / (7.209 x 10^-19 J)

After some math, we get λ ≈ 919.3 nm.

Now, what type of light is this? The human eye is sensitive to wavelengths in the range of approximately 400 to 700 nm, which falls in the visible spectrum. Since 919.3 nm is outside this range, it would be considered infrared light.

So, to answer your question, the maximum wavelength of light capable of ionizing Fe is approximately 919.3 nm, and this corresponds to infrared light. Time to warm up some leftovers with Fe-ionizing beams of humor!

To find the maximum wavelength of light capable of ionizing Fe, we can use the equation:

E = hc/λ

Where:
E is the ionization energy of Fe,
h is the Planck's constant (6.626 × 10^-34 J·s), and
c is the speed of light (2.998 × 10^8 m/s).
λ is the wavelength of light.

First, we need to convert the ionization energy from kJ/mol to J/atom:

Ionization energy (J/atom) = Ionization energy (kJ/mol) / Avogadro's number

where Avogadro's number is 6.022 × 10^23 mol^-1.

Ionization energy (J/atom) = 434 kJ/mol / (6.022 × 10^23 mol^-1) = 7.21 × 10^-19 J/atom

Now we can rearrange the equation to solve for wavelength:

λ = hc / E

λ = (6.626 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (7.21 × 10^-19 J/atom)

Calculating the equation, we get:

λ = 8.02 × 10^-7 meters

The maximum wavelength of light capable of ionizing Fe is approximately 8.02 × 10^-7 meters. This corresponds to light in the ultraviolet region of the electromagnetic spectrum.

To determine the maximum wavelength of light capable of ionizing Fe, you need to use the equation relating energy and wavelength:

E = hc/λ

where:
E is the energy of a photon,
h is Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light in a vacuum (2.998 x 10^8 m/s),
and λ is the wavelength of the light.

First, let's convert the ionization energy of Fe to joules:
Ionization energy = 434 kJ/mol = 434 x 10^3 J/mol.

Now, let's calculate the energy of a single photon:
1 mol of Fe atoms contains Avogadro's number of atoms, which is approximately 6.022 x 10^23 atoms. So the energy of a single photon can be calculated by dividing the ionization energy by Avogadro's number:

Energy per photon = (434 x 10^3 J/mol) / (6.022 x 10^23 atoms) = 7.211 x 10^-19 J.

Now, we can use the equation mentioned earlier to determine the maximum wavelength of light capable of ionizing Fe. Rearranging the equation, we have:

λ = hc/E

Substituting the values:

λ = (6.626 x 10^-34 J·s) × (2.998 x 10^8 m/s) / (7.211 x 10^-19 J)

Calculating this gives the maximum wavelength of light capable of ionizing Fe as approximately 271.8 nm (nanometers).

Now, let's determine the type of light associated with this wavelength. Light with a wavelength around 271.8 nm falls within the ultraviolet (UV) region of the electromagnetic spectrum. Therefore, the type of light capable of ionizing Fe is ultraviolet light.