Welcome to PhysLink.com - Your physics and astronomy online portal. Stay a while! Check out our extensive library of educational and reference materials. Also, check out our fun section!
What are quantum numbers? And how many are there?
Asked by: Sharma
Quantum numbers arise when we try to find the solution of the Schrödinger equation. Depending on the complexity the situation, determines how many quantum numbers there will be.
For example for a harmonic oscillator (a 1-D particle pond by a potential V=1/2kx^2 ) we only get one quantum number n and it represents the energy level of the harmonic oscillator. E=nhf.
For the 3-D one electron atom we get three n,l and ml. These represent the energy level, angular momentum and the angular moment in the z direction.
Another quantum number is ms and it represents the spin of the electron.
So as you can see as we extend the complexity of the situation, we get quantum numbers for everything, which is measurable.
Each electron has a set of four numbers, called quantum numbers, that specify it completely; no two electrons in the same atom can have the same four. That's a more precise statement of the Pauli exclusion principle.
Primary quantum number, which is given the symbol n,n tells you which of the "main" energy levels you're in.
The second quantum number is known as l. A value of l=0 corresponds to s, l=1 is p, l=2 is d, and so forth.
The third is magnetic quantum number m. l, along with n and the third quantum number, m, is responsible for determining the shape of an electron's probability cloud.
The fourth quantum number, s, does indeed pertain to an electron's spin. s only has two possible values+1/2 or-1/2.s= +1/2 means "spin up" and s= -1/2 means "spin down."
Within the level given by a particular n, l can take on only integer values from 0 to n-1.So when n is 1, l can only be 0, and that's why the first row has only s states. Then when n=2, l can be either 0 or 1, and that gives you s and p. Given a particular l, m is entitled to be any integer from minus l up to l. For example, when l=1, m can be -1, 0, or 1; those are your three p states. For a given l, there are 2l+1 different values of m.
Erector 10 Model Set
Today's Price: $21.00
Great Erector starter set that allows you to build 10 cool models. Buy it now! Deal ends at midnight!
Here are our physics & astronomy bestsellers:
Solar Science Kit
Mini Plasma Ball
Deluxe 3D Mirascope
Revolving Multi-Color Fiberoptic Light
Deluxe Water Rocket Set
Magnetic Levitator - Classic
Solar System Planetarium 4M Kit
Ultimate Chemistry Set CHEM C3000 v2.0
Worlds Strongest Magnets
Blue Fiber Optic Light