Answer :
Answer:
The ionization energy for a mole of hydrogen atoms is 1,312.17 kiloJoules.
Explanation:
Energy of the nth orbit by Bohr was given by:
[tex]E_n=-13.6\times \frac{Z^2}{n^2}eV[/tex]
where,
[tex]E_n[/tex] = energy of [tex]n^{th}[/tex] orbit
n = number of orbit
Z = atomic number
Energy of the first shell(n=1) in hydrogen atom:
Z = 1
[tex]E_1=-13.6\times \frac{1^2}{1^2}eV=-13.6 V[/tex]
Energy of the first shell(n=∞) in hydrogen atom:
Z = 1
[tex]E_{\infty }=-13.6\times \frac{1^2}{(\infty ^2)}eV=0[/tex]
Ionization energy of hydrogen atom,I.E : 1 → ∞
[tex]I.E=E_{\infty }-E_1=0-(-13.6 eV)=13.6 eV[/tex]
[tex]1 eV = 1.60218\times 10^{-19} J[/tex]
[tex]13.6 eV=13.6\times 1.60218\times 10^{-19} J=2.179\times 10^{-18} J[/tex]
[tex]2.179\times 10^{-18} J=2.179\times 10^{-21} kJ[/tex] (1kJ = 1000J)
Ionization energy of 1 mol = E
1 mol = [tex]N_A=6.022\times 10^{23} [/tex] atoms
[tex]E= 6.022\times 10^{23}\times 2.179\times 10^{-21} kJ=1,312.17 kJ[/tex]
The ionization energy for a mole of hydrogen atoms is 1,312.17 kiloJoules.