Problem Solving Strategies

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cOnnectOrTR 12

06:39

Hi @JohnRennie

John Rennie

@cOnnectOrTR12 Hi :-)

cOnnectOrTR 12

If a quantity x fall by say 10% then the new quantity is x-10%x or something else?

naturallyInconsistent

Yes, it will be 0.9x

John Rennie

If a quantity falls by 10% then it loses 10% of its original value.

So yes it reduces to x(1 - 0.1) and as naturallyInconsistent says that means it reduces to 0.9x.

cOnnectOrTR 12

Why do we say fall?

John Rennie

06:49

"fall" is just another way of saying "decrease"

cOnnectOrTR 12

Okay. I thought it meant something more.

naturallyInconsistent

07:06

because leaves fall down~

Naveen V

07:22

Can an electron which is in 3s orbital be present in a space which the 1s orbital electrons occupy (as I don't see any nodes there) ?

cOnnectOrTR 12

@naturallyInconsistent Yeah and so you fly up.

John Rennie

@NaveenV The electrons in orbitals are delocalised i.e. they are spread out across the whole orbital at the same time. You can think of the electrons as fuzzy clouds that spread out to fill the whole orbital.

naturallyInconsistent

@NaveenV Necessarily possible, because to get the orthogonality, there must be positive and negative overlaps to cancel.

John Rennie

And all the electrons overlap with all the other electrons.

Naveen V

So experimentally how do we differentiate them from inner electrons ?

John Rennie

07:28

By their energy.

For example the energy of a photon needed to eject a 3s electron from the atom is different from the energy needed to eject a 1s electron.

Naveen V

Oooh

And potentially can the s orbital electrons be present in the nucleus as well because there isn't any significant seperation which is shown in diagrams from orbitals and nucleus ? If yes if it's that close wouldn't they move towards each other due to electrostatic attraction which the orbitals cannot prevent ?

John Rennie

Yes it can occupy the same space as the nucleus.

For your second question see:

A: What prevents an atom's electrons from "collapsing" onto its protons?

As Mitchell says in his comment, this is related to the uncertainty principle. The uncertainty principle states that if you have some system with a position $x$ and a momentum $p$ then there is an uncertainty in the position, $\Delta x$, and an uncertainty in the momentum, $\Delta p$, related by...

naturallyInconsistent

We can see it as uncertainty principle, and we can also see it as kinetic energy. Trying to squeeze the electron's wavefunction so small as to be inside the nucleus, requires giving it a lot of kinetic energy. Either way, this is a quantum behaviour.

Naveen V

I will look into that thank you both for your answers !

3 hours later…

Naveen V

10:38

For semiconductors thermal energy can provide the necessary energy for an electron to jump from valence band to the (empty) conduction band and hence allowing conductance , but resistance increases with temperature so conductance might have been reduced ? Is one factor outweighing another factor so that conductance is happening ?

Naveen V

11:01

@JohnRennie From this answer , at r=0.53 the electron and the proton system is in a stable equilibrium and hence it has the minimum energy why doesn't the electron stay in the same distance and why do we need to introduce an orbital in which it has many places (which are not the minimum energy state) ?

naturallyInconsistent

11:50

@NaveenV The thermal excitation argument comes with resistance dropping with temperature. The resistance increasing with temperature applies for another other.

Naveen V

12:44

So why do we say that temperature increases resistance increases but in band theory its different

2 hours later…