Question

the first ionization energy of au (ie1) is 890.1 kj/mol. is light with a wavelength of 225 nm capable of ionizing a gold atom in the gas phase? justify your answer with a calculation.

Answer 1

Light with a wavelength of 225 nm is not capable of ionizing a gold atom in the gas phase.

Step-by-step explanation:

The first ionization energy of gold (Au) is 890.1 kJ/mol. In order to determine if light with a wavelength of 225 nm is capable of ionizing a gold atom in the gas phase, we need to compare the energy of the light with the ionization energy of gold.

The energy of a single photon can be calculated using the equation E = hc/λ, where E is energy, h is Planck's constant (
`6.626 x 10^-^3^4 J·s)`, c is the speed of light
`(2.998 x 10^8 m/s)`, and λ is the wavelength of the light in meters.

Converting the given wavelength to meters
`(225 nm = 2.25 x 10^-^7 m)`and substituting the values into the equation, we find that the energy of a single photon with a wavelength of 225 nm is
`8.83 x 10^-^1^9 J.`

Comparing this energy with the ionization energy of gold (890.1 kJ/mol =
`8.90 x 10^-^1^9`J per atom, since there are Avogadro's number of atoms in a mole), we see that the energy of the light is less than the ionization energy of gold. Therefore, light with a wavelength of 225 nm is not capable of ionizing a gold atom in the gas phase.