Atomic theory in another planet - problem

In summary: I think this will be considered a correct answerIn summary, there is a discussion about a hypothetical planet where the spin numbers and magnetic quantum numbers are different than on Earth. The conversation delves into how the periodic table and energy level diagram may look like on this planet. The participants also discuss the significance of the number of subshell configurations and the formula for finding the number of electrons in each shell. The conversation ends with a suggestion to stick to the Earth-based ordering of energy levels.
  • #1
naren11
19
0
In a planet, if the spin numbers were +1/2, 0 , and -1/2 and their magnetic quantum numbers take the values 0, 1, 2,...L

( Everything else including the ordering and naming of the orbits are same except the spin numbers and the magnetic quantum numbers as provided above.)

how would the perodic table and the energy level diagram may look like?

thanks!
 
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  • #2
There are 3 possible spin states (instead of 2) and "l+1" (instead of "2l+1") values for [itex] m_{l} [/itex]...

Does that help in any way?

Daniel.
 
  • #3
im not sure if that helps..
In our planet Earth , there are only 2 spin states which are +1/2 and
-1/2 and the magnetic quantum numbers are -L to +L (postive to negative)

Now, if there were an additional spin state which is 0 in another planet and the magnetic quantum numbers are only whole numbers (0,1,2...)

how would theperodic table has to be modified and the energy level diagram?
 
  • #4
[tex] n=0\rightarrow \mbox{impossible} [/tex]
[tex] n=1\rightarrow l=0\rightarrow m_{l}=0 [/tex]
[tex] n=2\rightarrow l=1\rightarrow m_{l}=0 [/tex]
[tex] n=2\rightarrow l=1\rightarrow m_{l}=1 [/tex]
[tex] n=2\rightarrow l=0\rightarrow m_{l}=0 [/tex]
[tex] n=3\rightarrow l=2\rightarrow m_{l}=2 [/tex]
[tex] n=3\rightarrow l=2\rightarrow m_{l}=1 [/tex]
[tex] n=3\rightarrow l=2\rightarrow m_{l}=0 [/tex]
[tex] n=3\rightarrow l=1\rightarrow m_{l}=1 [/tex]
[tex] n=3\rightarrow l=1\rightarrow m_{l}=0 [/tex]
[tex] n=3\rightarrow l=0\rightarrow m_{l}=0 [/tex]

Build the rest.Keep in mid that for every subshell,u can have max.3 electrons...

Daniel.
 
  • #5
What Dexter's trying to get you to do (if I may attempt to read his mind :wink:) is get you to count how many allowed configurations exist for a particular subshell.

How many 2p configurations has he built (n=2, l=1, ml = 0,1 and ms = +, 0, -) ? In fact, he has even written out, in general how many configurations you will have for a particular valence subshell. Compare this with the number of configurations in a "normal" (meaning, on planet Earth) subshell [clearly, the number is 2*(2l+1) on Earth; what about the other planet?].

So, the obvious question to then ask is "what is the significance of the number of subshell configurations ?" Look at the different groups in your periodic table and see if you can find the relationship.
 
  • #6
[tex] n=0\rightarrow \mbox{impossible} [/tex]
[tex] n=1\rightarrow l=0\rightarrow m_{l}=0 [/tex] 1s
[tex] n=2\rightarrow l=1\rightarrow m_{l}=0,1 [/tex] 2p
[tex] n=2\rightarrow l=0\rightarrow m_{l}=0 [/tex] 2s
[tex] n=3\rightarrow l=2\rightarrow m_{l}=0,1,2[/tex] 3d
[tex] n=3\rightarrow l=1\rightarrow m_{l}=0,1 [/tex] 3p
[tex] n=3\rightarrow l=0\rightarrow m_{l}=0 [/tex] 3s
[tex] n=4\rightarrow l=3\rightarrow m_{l}=0,1,2,3 [/tex] 4f
[tex] n=4\rightarrow l=2\rightarrow m_{l}=0,1,2 [/tex] 4d
[tex] n=4\rightarrow l=1\rightarrow m_{l}=0,1 [/tex] 4p
[tex] n=4\rightarrow l=0\rightarrow m_{l}=0 [/tex] 4s

ok, [tex] l=0\rightarrow s > orbital [/tex]
[tex] l=1\rightarrow p > orbital [/tex]
[tex] l=2\rightarrow d > orbital [/tex]
[tex] l=3\rightarrow f > orbital [/tex]

i guess iam right so far..

what is the formula we use to find the number of electrons in this case?
if u don't mind, could you show me how would it look like for sodium?
 
Last edited:
  • #7
[tex] _{11}^{23}Na:1s^{3}2s^{3}2p^{5} [/tex]

Daniel.
 
  • #8
the p shell would have maximum of 7 electrons?
d > 10 electrons
f > 15 ?
 
  • #9
naren11 said:
the p shell would have maximum of 7 electrons?
d > 10 electrons
f > 15 ?
No; how did you get these numbers ? You are making a mistake somewhere. The first two numbers are not even multiples of 3 (which they will have to be, since each m_l has 3 allowed values of m_s). I've written the formula which Dexter suggested, in my previous post. You just have to modify this with the new numbers for m_l, m_s.
 
  • #10
ok, so this is how would the electron config. look like..?

[tex] 1s^{3}2s^{3}2p^{6}3s^{3}3p^{6}4s^{3}3d^{9}4p^{6}4d^{9}4f^{12} [/tex]
 
  • #11
Correct ! And don't forget 5s, 5p and 6s. If you're sticking with the Earth based ordering, these would figure before the 4f.

Of course, the ordering may change but that is surely beyond the scope of this problem.
 
  • #12
im only doing upto fourth energy level. Just to make sure, since this is not an Earth based ordering, 5s, 5p, and 6s wouldn't come..right?

thanks alot
 
  • #13
naren11 said:
im only doing upto fourth energy level.
You mean fourth shell. There is a difference (except in the Bohr Model)

Just to make sure, since this is not an Earth based ordering, 5s, 5p, and 6s wouldn't come..right?

thanks alot
This is hard to tell. If you are setting an energy cutoff, you will have to calculate the energies of the different states in the other planet. This is not a simple thing to do, and is surely beyond the scope of this problem.

I suggest you stick to Earth based ordering (even if it doesn't apply in the other planet) and put in 5s, 5p and 6s in the correct (earth-based) places.
 

Related to Atomic theory in another planet - problem

1. What is atomic theory and how does it apply to other planets?

Atomic theory is the scientific explanation of the nature and behavior of matter. It states that all matter is made up of tiny particles called atoms, and that these atoms are the building blocks of everything in the universe. This theory applies to other planets because the laws of physics and chemistry that govern the behavior of atoms are universal.

2. Are the elements and atoms found on other planets the same as those on Earth?

It is likely that the elements and atoms found on other planets are similar to those found on Earth, as they are created through the same processes in the universe. However, there may be some variations due to different environmental conditions and the formation of the planet.

3. How does the atomic structure of other planets affect their physical and chemical properties?

The atomic structure of a planet, including the types and arrangement of its atoms, can greatly impact its physical and chemical properties. For example, the density, melting point, and reactivity of a planet's elements will be influenced by its atomic structure.

4. Can atomic theory be used to explain the formation and evolution of other planets?

Yes, atomic theory can be applied to understand the formation and evolution of other planets. The formation of planets involves the accumulation of matter, and the evolution of planets is influenced by the interactions and transformations of different elements and compounds.

5. Is there any evidence of atomic theory on other planets?

While we do not have direct evidence of atomic theory on other planets, the laws and principles of atomic theory have been observed and proven in the study of our own solar system and beyond. This provides strong evidence that the same principles apply to other planets as well.

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