Ionization Energy equation

In summary, the conversation discusses the process of ionization and how it relates to the energy of a valence level n. The equation E= -2.178 x 10^-18 (Z^2/n^2) is used to calculate the ionization energy of hydrogen in units of kJ/mol. The calculation is confirmed to be consistent with the experimental value of 1310 kJ/mol. There is a small error in the substitution of the formula, as the correct equation should be 1/n_1^2 - 1/n_2^2 = 1/1^2 - 1/\infty^2 = 1 - 0 = 1. This conversation may be similar to a previous one
  • #1
erik05
50
0
Hello everybody, just wondering if anyone could point me in the right direction for this question. Please and thanks.

1) Since the ionisation process takes an electron from its ground state to the zero level of the energy scale, the ground state energy calculated for the electron of the hydrogen atom can be compared to the negative of its ionization energy (IE). Use the equation E= -2.178 x 10^-18 (Z^2/n^2) for energy of a valence level n, to build a equation that can be used to calculate the ionisation energy of H in units of kJ/mol.

So far what I have is...

Since Z represents the atomic number and the atomic number for hydrogen is 1:

E= -2.178 x 10^-18 (1^2/n^2)

so equation is E= -2.178 x 10^-18 (1/n^2)

2) Use equation to calculate ionization IE for H and confirm that value obtained is consistent with the experimental value of 1310 kJ/mol.

E= -2.178 x 10^-18 (1/ (1-0)^2) since electron going from ground state to zero level therefore:
E= -2.178 x 10^-18 J per 1 atom. So then,

E= -2.178 x 10^-18 J/atom x (6.022 x 10^23 atom/mol) / 1000
= -1312 kJ/mol
 
Physics news on Phys.org
  • #2
Your answer is correct, but there is a tiny error in the way you've substituted in the formula.

Where did you get 1/(1-0)^2 from ? The ionization energy is the energy difference between the first shell and an infinitely removed shell. So the shell dependence goes like [itex]1/n_1^2 - 1/n_2^2 = 1/1^2 - 1/\infty^2 = 1 - 0 = 1[/itex]. The rest is good.

PS : Didn't I answer an almost identical question recently ?

EDIT : Found it : https://www.physicsforums.com/showthread.php?t=93440
 
  • #3


The equation you have constructed is correct. To calculate the ionization energy of hydrogen, we use the equation E= -2.178 x 10^-18 (Z^2/n^2), where Z=1 for hydrogen and n is the principal quantum number of the valence level. In this case, n=1 since we are considering the ground state of hydrogen.

To confirm the value obtained, we can convert the energy from Joules to kJ/mol by multiplying it by Avogadro's number (6.022 x 10^23 atoms/mol) and dividing by 1000 to get the energy in kJ/mol. This results in a value of -1312 kJ/mol, which is consistent with the experimental value of 1310 kJ/mol.

The negative sign in the equation indicates that the ionization energy is the amount of energy needed to remove an electron from the atom. This value is always positive, so we use the negative sign to indicate that energy is being released from the atom during ionization.

In summary, the ionization energy equation E= -2.178 x 10^-18 (Z^2/n^2) can be used to calculate the ionization energy of hydrogen in units of kJ/mol and the value obtained using this equation is consistent with the experimental value. This equation can also be used for other atoms, with Z representing the atomic number and n representing the principal quantum number of the valence level.
 

What is the Ionization Energy equation?

The Ionization Energy equation is a mathematical formula used to calculate the amount of energy required to remove an electron from an atom or molecule in its ground state.

Why is the Ionization Energy equation important?

The Ionization Energy equation helps us understand the stability and reactivity of atoms and molecules. It also plays a crucial role in fields such as chemistry, physics, and astronomy.

What are the variables in the Ionization Energy equation?

The variables in the Ionization Energy equation are the charge of the nucleus (Z), the radius of the atom (r), and the ionization energy (Ei).

How is the Ionization Energy equation used in real-world applications?

The Ionization Energy equation is used in various applications such as studying atomic and molecular structures, predicting chemical reactions, and developing new materials and technologies.

How does the Ionization Energy equation relate to the periodic table?

The Ionization Energy equation is closely related to the periodic table as it helps us understand the trends in ionization energy across the elements. For example, ionization energy generally increases from left to right on the periodic table, and decreases from top to bottom.

Similar threads

  • Biology and Chemistry Homework Help
Replies
2
Views
1K
  • Biology and Chemistry Homework Help
Replies
6
Views
1K
  • Biology and Chemistry Homework Help
Replies
8
Views
9K
  • Biology and Chemistry Homework Help
Replies
5
Views
2K
Replies
3
Views
4K
  • Biology and Chemistry Homework Help
Replies
5
Views
7K
  • Atomic and Condensed Matter
Replies
18
Views
1K
  • Biology and Chemistry Homework Help
Replies
2
Views
59K
  • Biology and Chemistry Homework Help
Replies
4
Views
2K
  • Biology and Chemistry Homework Help
Replies
6
Views
3K
Back
Top