Do you graph the energy levels of a ##1s^1## atom the same as a ##1s^2## atom?

In summary, the energy levels of a ##1s^1## atom (hydrogen) and a ##1s^2## atom (helium) are graphed differently due to the presence of additional electrons in the ##1s^2## atom. The ##1s^2## configuration has electron-electron repulsion and shielding effects that influence the energy levels, leading to differences in how the two atoms are represented in energy level diagrams.
  • #1
Danielk010
34
4
Homework Statement
Draw an energy-level diagram showing the lowest four levels of singly ionized helium. Show all
possible transitions from the levels and label each transition with its wavelength.
Relevant Equations
##E_n = \frac {-me^2} {32\pi^2\varepsilon_0^2n^2}##
From the first equation, there are 5 constants, e, ##\pi##, ##\varepsilon_0##, ##n^2##, and 32. The only difference is m, where helium has around four times the mass of hydrogen. What I don't get is if there is a difference between the energy levels of the hydrogen and the ionized hellium? Also I get that helium is ionized in this case so would the atom have an electric configuration of ##1s^1##? Thank you for any help.
 
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  • #2
Danielk010 said:
What I don't get is if there is a difference between the energy levels of the hydrogen and the ionized hellium?
What is ##Z## for hydrogen and helium? How do the energy levels depend on ##Z##?
 
  • #3
kuruman said:
What is ##Z## for hydrogen and helium? How do the energy levels depend on ##Z##?
Z for hydrogen is 1 and Z for helium is 2. The higher the Z, the higher the energy level. I got the equation: ##E_n = E_0 * \frac {Z^2} {n^2}##
 
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  • #4
What does higher mean here? These levels are usually measured relative to zero at ionization (hencenegative). Also be aware that the mass is the "reduced mass" which changes a little.
 
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  • #5
Danielk010 said:
Z for hydrogen is 1 and Z for helium is 2. The higher the Z, the higher the energy level. I got the equation: ##E_n =##E = E_0 * \frac {Z^2} {n^2}##
hutchphd said:
What does higher mean here? These levels are usually measured relative to zero at ionization (hencenegative). Also be aware that the mass is the "reduced mass" which changes a little.

So the ##E_0## value would be increased by the Z, nuclear charge and decreased by n, number of electrons. If ##E_0## is negative then it would be vice versa, I think? Since the hellium is ionized so n = 1 and Z = 2, that means it is ##4 * E_0##, right?
 
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  • #6
Danielk010 said:
If ##E_0## is negative then it would be vice versa, I think?
I don't know what you are trying to say here. Vice versa is used to indicate that the reverse of what you have said is also true. For example 'people can perform some tasks better than machines can and vice versa' means that machines can perform some tasks better than people can.

So are you saying that if ##E_0## is negative, then it would be . . . positive?
 
  • #7
kuruman said:
I don't know what you are trying to say here. Vice versa is used to indicate that the reverse of what you have said is also true. For example 'people can perform some tasks better than machines can and vice versa' means that machines can perform some tasks better than people can.

So are you saying that if ##E_0## is negative, then it would be . . . positive?
Sorry for the confusion.

What I meant is that when ##E_0## is negative. If Z increased then ##E_0## would decrease. If n increased, ##E_0## would increase as well.

When ##E_0## is positive, when Z increased, ##E_0## would also increase. When n increased, ##E_0## would decrease.
 
  • #8
When the magnitude of a negative number increases, the number decreases because it moves farther away from zero. It is more descriptive to say that if ##Z## is increased, the ground state ##E_0## will lie deeper.
 
  • #9
What is 1s2?
 
  • #10
pines-demon said:
What is 1s2?
The electronic configuration
 
  • #11
kuruman said:
When the magnitude of a negative number increases, the number decreases because it moves farther away from zero. It is more descriptive to say that if ##Z## is increased, the ground state ##E_0## will lie deeper.
Ok thank you
 
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  • #12
Danielk010 said:
The electronic configuration
Ah right. I do not get the question, but as for the title, we tend to represent orbitals for a single particle (electron) not for two.
 
  • #13
Ok thank you. I think I got the idea
 

FAQ: Do you graph the energy levels of a ##1s^1## atom the same as a ##1s^2## atom?

1. What is the difference between a 1s1 and a 1s2 atom?

A 1s1 atom has one electron in the 1s orbital, while a 1s2 atom has two electrons in the same orbital. The presence of two electrons in the 1s orbital for the 1s2 atom introduces electron-electron interactions that can affect the energy levels and the overall stability of the atom.

2. Do both atoms occupy the same energy level?

Yes, both the 1s1 and 1s2 atoms occupy the same principal energy level, which is the 1s level. However, the energy of the 1s2 atom is slightly lower due to electron-electron repulsion and the effects of electron shielding, which can stabilize the atom further.

3. How are the energy levels represented graphically for these atoms?

The energy levels for both 1s1 and 1s2 atoms can be represented on the same graph, typically as a single line for the 1s level. However, the 1s2 level may be depicted with additional annotations or shading to indicate the presence of two electrons and the associated interactions.

4. Does the electron configuration affect the graphing of energy levels?

While the electron configuration does not change the fundamental energy level structure, it does influence how we interpret the stability and energy of the atom. For example, the 1s2 configuration is generally more stable than the 1s1 configuration, which can be reflected in the graphical representation by indicating lower energy for the filled orbital.

5. Are there any implications for chemical behavior based on these energy levels?

Yes, the electron configuration has significant implications for chemical behavior. A 1s1 atom is often more reactive because it has an unpaired electron that can participate in bonding, while a 1s2 atom is more stable and less likely to react due to its filled 1s orbital. This difference can be illustrated in energy level graphs by showing how the energy levels influence reactivity and bonding tendencies.

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