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

Answer:

oh ya z

Explanation:

i did it in my head

Answer 2

Answer:

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

Explanation:

$E_n = -(2.18 10-18 J)\times \frac{Z^2}{n^2}$

Z = atomic mass

n = principal quantum number

Energy of the electron in n=1,

$E_1= -(2.18 10^{-18} J)\times \frac{4^2}{1^2}=-3.488\times 10^{-17} J$

Energy of the electron in n = ∞

$E_{\infty}= -(2.18 10^{-18} J)\times \frac{2^2}{\infty ^2}=0 J$

Ionization energy of the $He^+$ ion:

$I.E=E_{infty}-E_1=0-(-3.488\times 10^{-17} J)=3.488\times 10^{-17} J$

$I.E=3.488\times 10^{-20} kJ$

To convert in into kj/mol multiply it with $N_A=6.022\times 10^{23} mol^{-1}$

$I.E=3.488\times 10^{-20} kJ\times 6.022\times 10^{23} mol^{-1}=21,004.73kJ/mol$