A hydrogen-like ion is an ion containing only one electron. The energy of the electron in a hydrogen-like ion is given by:
En=-(2.18x10^(-18)J)Z^2(1/(n^2))
where n is the principal quantum number and Z is the atomic number of the element.
Calculate the ionization energy (in kJ/mol) of the He+ ion.
???
I think I did this for you last night.
Z = 2^2
n = 1. Punch into the calculator and move on.
if you plug in
Z=2^2
n=1
its wrong and i don't knwo why
It is -8,72 x 10^-21 kJ
Reason: After punching in those values you then have to convert that answer from J to kJ which 1kJ=1000J
STILL WRONG
Still figuring it out to this day huh?
To calculate the ionization energy of the He+ ion, we need to find the energy difference between the ground state and the ionized state.
The ground state of the He+ ion corresponds to the electron being in the lowest energy level, which is the n=1 state. We can substitute n=1 and Z=2 (since helium has an atomic number of 2) into the given equation to find the energy of the ground state.
E1 = -(2.18x10^(-18) J)(2^2)(1/(1^2))
= -(2.18x10^(-18) J)(4)
= -8.72x10^(-18) J
Now, we need to find the energy of the ionized state, where the electron is completely removed from the He+ ion. In this case, the electron is at an infinitely far distance from the nucleus, so the energy is zero.
The ionization energy is equal to the energy difference between the ground state and the ionized state. Therefore:
Ionization energy = 0 - (-8.72x10^(-18) J)
= 8.72x10^(-18) J
Lastly, we need to convert the ionization energy from joules to kilojoules and from per ion to per mole. The conversion factor from joules to kilojoules is 1 kJ = 1000 J, and since we are dealing with one ion, the ionization energy per mole is the same as the ionization energy for a single ion.
Ionization energy = 8.72x10^(-18) J * (1 kJ / 1000 J)
= 8.72x10^(-21) kJ
Therefore, the ionization energy of the He+ ion is approximately 8.72x10^(-21) kJ/mol.