Question

A hydrogen-like ion is an ion containing only one electron. The energies of the electron in a hydrogen-like ion are given by the following equation where n is the principal quantum number and Z is the atomic number of the element. En = −(2.18 10-18 J)Z2 (1/n2) Calculate the ionization energy (in kJ/mol) of the He+ ion.

Answer 1

oh ya z

Step-by-step explanation:

i did it in my head

Answer 2

The ionization energy (in kJ/mol) of the helium ion is 21,004.73 kJ/mol .

Step-by-step explanation:

`E_n = -(2.18 10-18 J)* (Z^2)/(n^2)`

Z = atomic mass

n = principal quantum number

Energy of the electron in n=1,

`E_1= -(2.18 10^(-18) J)* (4^2)/(1^2)=-3.488* 10^(-17) J`

Energy of the electron in n = ∞

`E_(\infty)= -(2.18 10^(-18) J)* (2^2)/(\infty ^2)=0 J`

Ionization energy of the
`He^+` ion:

`I.E=E_(infty)-E_1=0-(-3.488* 10^(-17) J)=3.488* 10^(-17) J`

`I.E=3.488* 10^(-20) kJ`

To convert in into kj/mol multiply it with
`N_A=6.022* 10^(23) mol^(-1)`

`I.E=3.488* 10^(-20) kJ* 6.022* 10^(23) mol^(-1)=21,004.73kJ/mol`