Chemistry - Electron Structures in Atoms (26 of 40) Radial Probability Density Function: S-Orbital
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- Опубликовано: 21 дек 2024
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In this video I will explain the radial probability density function for the s-orbitals.
EXCELENT!! Better explanation than any textbook of inorganic Chem. Very Clear!
+Pablo Cardella try cengage textbooks
THANK YOU SO MUCH I WAS STRUGGLING LIKE CRAZY THIS MAKES SO MUCH SENSE!! yay to not failing chemistry :)
finally!!! An english speaking video about this
Thank you so much! This is the only video that truly explained this concept the easiest and correct way
Right
You explained it like a pro . Thanks bruh you helped a lot.❤️
Glad it helped
Thank you for spending the time to make this video. !The visuals really help
Perfect explanation ever!
Glad you think so!
Your explanation was amazing.
Thank you
These videos are very powerful.. Thanks, Prof.
You are very welcome
tomorrow our test
I think its helpful for me thanks a lot 🇮🇳
I am Grateful For you
Helped a lot!!!!!!!!!!
Came soo Confused
Now going Clear
You're Welcome!
@@MichelvanBiezen :)
Actually this was one of the questions in the previous semester........and I have no clue
We wish to verify that an infinite potential well of width L has eigenfunctions
given by
2 φn(x) = sin(knx), (15) L
with energy En = n2kn
2/2m, where kn = (n + 1)π/L. We can do so by plugging the eigenfunctions into the energy eigenvalue equation:
n2 d2ψ Eψˆ = Eψ ⇒ − = Eψ, (16) 2m dx2
where we have restricted ourselves to 0 ≤ x ≤ L, so V (x) = 0. The left hand side is given
by
n2 d2ψ n2 d2 2 n2k2 2 − = − sin(knx) = n sin(knx) = Enφn, (17) 2m dx2 2m dx2 L 2m L
so our eigenfunctions are indeed solutions to the system. The fact that kn = (n + 1)π/L
follows from the need to satisfy the boundary conditions φn(0) = φn(L) = 0.
This is mind boggling
thank you so much , it did make the concept clear sir 💯😊
Great! Glad you found our videos. 🙂
This is a really elaborate and precise educational video on s orbitals. It"d be great if you could make a video on the nodes of p orbitals too.
I don't know how I got here but I'm glad I did.
can anyone explain the difference exactly between the pdf and the one above it?
The bottom was an attempt to draw a 3-dimensional picture of the various orbitals and the probability density of the electrons. The middle row is a depiction of the Schrodinger equation for the electron positions. The top row is the graph depicting the probability of finding the electron at that range. We have a playlist with dozens of videos in the quantum mechanics section that desribe all that in mathematical detail.
@@MichelvanBiezenthank u. i’m taking a intro to chemistry class and we don’t really deal with the mathematical part in this class. my problem is making sense of what kind of probability the middle and top row show, as they both seem to show a probability based on the distance from the nucleus but show entirely different results
The Shrodinger equation (middle row) does not show probability. It simply represents an energy equation which can be used to calculate the probability seen in the top row.
Can a planet atmosphere be a model for 1S orbital?
Can you explain why both graph types (P and Psi^2) have different values at r/a = 0? What is missing from the Psi^2 function to be the probability? Can the electron reside in the nucleus ?
have you got an answer yet?
Good morning professor,
I just wanted to ask you since I have a Chemistry quiz next week, how we could switch from the probability density functions, to the probability graphs. Thank you for your amazing videos!
+Hermione Granger
The Schrodinger equation describing the electron in the innermost orbit for hydrogen is:
Psi = (1/sqrt(pi) * a^(3/2))* e^(-r/a)
when you square that equation you will get the probability density function describing the most probable location for the electron
Probability = (Psi)^2
At that point it is a matter of knowing how to graph an e^(-x) function (time to brush up on graphing exponential functions)
+Michel van Biezen Ah yes that I understood, I don't know how to deduce the upper graph in your video from the lower one, though. For the 1s orbital the 1st graph is a little bell shaped (with a maximum) while the one under it looks like a hyperbola.
Thank you for answering me, it is incredibly kind of you!!
6:31 it's always possible but probability is very very low
No , it's a node. probability is 0 over there.
Nah bro probability tends to zero not equal to zero😊@@yashyelmame1460
Thank you so much for this video. But I'm confused as to the meaning of |phi|^2 and the Radial distribution function for the hydrogen atom. R(r) peaks at the Bohr radius, meaning the greatest chance of finding an electron is at this radius. |phi|^2 peaks at r=0, meaning the electron is mostly to be found at or in the nucleus. Both statements cannot be true os where's my confusion? Thanks again!
It wasn't the purpose of going into those types of details in this vides If you want to understand the details, you can find them here in this 60 video playlist that explains all the details. PHYSICS 66.5 QUANTUM MECHANICS: THE HYDROGEN ATOM
@@MichelvanBiezen Thank you for the fast reply. I saw the graphs for the Radial and |phi|^2 functions in this video, hence my questions. Thank you for the video referral.
Great explanation. Thankyou sir
You're most welcome
Greetings from China ,thank u so much for for teaching ,thank u Michel
Our pleasure!
Isn't the Bohr radius about 1/2 an Angstrom? Are these supposed to be multiples of the Bohr radius or Angstroms?
The Bohr radius is about 53 nanometers, which is about 0.53 Angstroms.
amazing! It's very easy tot understand now, thank you!
I just got saved.THanks sir
Happy to help
Thank you sir you have deep concepts of the subject on which you deliver the lecture
you are more than a genius!!!!
Thank u sooooooo much for making this informative & helpful video! Please keep up making more videos !
how many planar nodes and radial nodes are there in a 4p orbital? by the way, this is a very clear explanation of the s orbitals. :)
Planar nodes = Radial nodes = n - l - 1 = 4 - 1 - 1 = 2. look up quantum numbers.
so all atoms have the same pattern of orbitals 1s 2s 2p etc. but each atom has different energy levels. So within the eg 2s orbital, there are different numbers or different distances of the energy levels within different atoms of elements? (since energy levels are unique to each atom)
You are correct. The equations work for the Bohr atom and singly ionized helium, etc.
And what is a formula for the distribution function?
Details on that can be found here: PHYSICS 66.5 QUANTUM MECHANICS: THE HYDROGEN ATOM
What about the probability density for p, d, f orbitals sir?
For more mathematical details, you can go to this playlist where all that is carefully explained. PHYSICS 66.5 QUANTUM MECHANICS: THE HYDROGEN
if the probability of n=1very near the nucleus tend to zero, why the density of probability there is maximum?
The density of probability is just a mathematical concept. The real value you are looking for is the probability of finding the particle, which as you can see goes to zero at the center. If you want to understand that better you can watch the videos in the playlist: PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Happy Xmas Michel, thanks for all your sharing and making us understand modern physics.
Good explanation ! Thanks sir
Thank you sir❤
You are welcome.
the more electron shells, the more space the atom takes up
Best video on this topic
Nice explanation sir
This video is actually good but how come the probability of finding an electron become s zero at some points, as it is always uncertain we can't directly say that there's zero probability at some points right
The concept of the probability of zero at "a point" is a purely mathematical concept and does not exist in the real world. For example, when you throw a ball straight up, is there a "point" where the ball reaches zero velocity before it comes back down. Mathematically, yes, but in the real world no. The ball spends zero time at its highest point.
@@MichelvanBiezen thank u sir ,I got it
Nice video sir .. thanks
Awesome ! cleared all my queries! u r the best! Please come to India and teach :P
Is this the same thing as a wave function of the electron?
What is depicted is the PROBABILITY of finding the electron which is based on the wave function.
@@MichelvanBiezen what exactly is the difference if its alright that I ask
The wave function is described by the Schrodinger equation and does not really have a physical meaning. But when we square the wave function and normalize it (so that the integration over all space equals 1), then it gives us the probability of finding the electron in any one place. So it is the probability functions that are graphed and which give us the information we are looking for.
Thank you for the nice video! But there is one point that might be revised.
In approx. 6 min, the teacher said that there is no probability of existence in the tail of the probability function.
But as r(distance) increases, the probability goes nearly zero but it cannot be said "it is zero."
great explanation! thanks!
thank's for your great concept.
Thank you sir!!
Most welcome!
Thank you sir! Thanks for keeping it simple...
Thank you
You're welcome 🙂
Amazing !
Great, thanks!
super helpful!
Thank you so much
You're most welcome
Such a great video! Thank you so very much :)
Thank you.
Thank you very much sir.... it helps me to understand clearly....
Although he kind of implies that electrons "revolve" around the nucleus of an atom the way planets revolve around the sun. This isn't really what's happening.
BlackWisps,
Actually this implies that electrons don't revolve around the nucleus like a planet around the Sun.
The probability density function is simply an indication as to where you are more likely to find the electron at any point in time. The S-orbital do have a spherical shell which means that there is no dependency on angle, only on radius.
Thanks buddy
Thanks sir
awesome
Hey i thought you were expert in astrophysic.s
🔥
Yes bro is a pookie 🎀
👍
Misleading concept.
Im in 7th grade this is way to complicated for me.
One day you will understand all this.
When you are stuck in chemistry try to tackle by thinking from physics or mathematics perspective
Thank you so much.
Great explanation ! thanks !