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.
???
C'mon. Substitute and calculate. Just punch in the numbers on the calculator. Z is 2 (and that is squared). n = 1 isn't it.
To calculate the ionization energy of the He+ ion, we can use the formula for the energy of the electron in a hydrogen-like ion:
En=-(2.18x10^(-18)J)Z^2(1/(n^2))
In this case, we have Z = 2 (atomic number of helium) and n = 1 (principal quantum number). Now we substitute these values into the formula:
E1=-(2.18x10^(-18)J)(2^2)(1/(1^2))
Simplifying the formula:
E1=-(2.18x10^(-18)J)(4)(1/1)
E1=-(8.72x10^(-18)J)
To convert this value from joules to kilojoules, we divide by 1000:
E1=-(8.72x10^(-18)J)/1000
E1=-(8.72x10^(-21)kJ)
So, the ionization energy of the He+ ion is -8.72x10^(-21) kJ.