In energy terms, ionization of an electron in an atom corresponds to the transition from whatever quantum state the electron is in to an energy of 0 KJ/mole. Calculate the energy in joules needed to remove one electron in the n=1 state from a hydrogen atom.

I know En of 1 = -1312 KJ/mole
so delta En = | 0+1312 |= 1312 KJ/mol

1312 KJ/mol x 1mol/6.022 x 10^23 particles x 1000joules/KJ

is this the correct why to approach this problem? Are my steps correct?

Yes but I would have gone about it another way.

1312000/6.022 x 10^23 = 2.18 x 10^-18 J/atom by your calculations.
I would use
delta E = 2.180 x 10^-18 J (1/N1^2 -1/N2^2)
For N2 = infinity, 1/N^2 is zero and 1/N1^2 = 1; therefore, E = 2.180 x 10^18 joules/atom

Your steps are correct, but there is a small mistake in your conversion factor. Let's go through the correct calculation step-by-step:

1. Start with the energy change (ΔE) between the n=1 state and 0 KJ/mol: ΔE = |0 - (-1312)| = 1312 KJ/mol.

2. Convert the energy change from kilojoules per mole to joules per particle:
- Remember that 1 mole contains 6.022 x 10^23 particles, so you can use the conversion factor 1 mol / 6.022 x 10^23 particles.

ΔE = 1312 KJ/mol x (1000 J / 1 KJ) x (1 mol / 6.022 x 10^23 particles)

3. Multiply the conversion factors and perform the calculation:
ΔE = 1312 KJ/mol x (1000 J / 1 KJ) x (1 mol / 6.022 x 10^23 particles)
= 1312 x 1000 / 6.022 x 10^23
≈ 2.18 x 10^-18 J

Therefore, the energy needed to remove one electron in the n=1 state from a hydrogen atom is approximately 2.18 x 10^-18 J.

Yes, your approach is correct. To calculate the energy needed to remove one electron from the n=1 state of a hydrogen atom, you can use the formula:

ΔE = |E_final - E_initial|

Where:
E_final is the final energy state (in this case 0 KJ/mol)
E_initial is the initial energy state (in this case -1312 KJ/mol as given for the n=1 state of a hydrogen atom)

So, ΔE = |0 - (-1312)| = 1312 KJ/mol

To convert this energy from kilojoules per mole to joules per particle, you can use the conversion factor:

1 mol / 6.022 x 10^23 particles

So, the energy needed to remove one electron from the n=1 state of a hydrogen atom is:

1312 KJ/mol x (1 mol / 6.022 x 10^23 particles) = 2.18 x 10^-18 joules per particle

Therefore, the energy needed to remove one electron in the n=1 state from a hydrogen atom is approximately 2.18 x 10^-18 joules.