4d there are four types of quantum numbers: 1st: principle quantum number; relates to which electron shell your election is. its symbol is n, and it can be any number like 1,2,3,4....etc. here, n = 4. 2nd: azimuthal; gives the orbital angular momentum which specifies the shape of the orbital you're talking about. its symbol is lower-case L, or l, and can be any number from 0 up until one less than your n value. here, because n=4, l can be 0,1,2 or 3, corresponding to s,p,d or f orbitals respectively (you just have to memorize that part). so here, because it's 4d, and d corresponds to l = 2, our azimuthal quantum number here is l = 2. 3rd: magnetic; determines which one of the set of orbitals you're talking about. its symbol is ml. this can be anything from -l up to +l. here, because l is 2, we know that ml can be -2, -1, 0, +1, or +2. this makes sense because we know there are 5 types of d-orbitals. however, we don't have enough information to determine what ml is here of those five. (another example to think about - how many p-orbitals are there? a chem textbook will tell you there are three, and draw them all pointing different directions - px, py, pz. the azimuthal quantum number l for p-orbitals is 1. so ml can be -1, 0, or +1 = three different types. the math works out!) 4th: spin quantum number; tells whether the electron you're talking about is in spin-down or spin-up configuration. its symbol is ms. this number can always be either -1/2 or +1/2. again, you don't know which one you're talking about here - you don't have enough information. hope that helps!
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using contraction and expansion
electrical engineers and quantum mechanics use them.
It is the total of those numbers divided by four.
We can think time as a 4D object, but we cannot visualize so easily a 4D object. But surely we know that a 4D object cannot live inside the 4D space, it will live in the 5th dimension space. We know that we can calculate the hyper-volumes by using integration (in our case) over a R4 domain which is not so easy to be visualize also. For example by hand we can construct a R3domain by using the xyz-coordinate system.
Molecular biology, quantum physics, cosmology and physical chemistry are four examples.