3f ( 3 only has the d orbital final )
and
2d ( 2p is the final orbital on the 2 level )
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The orbital designations 3f and 2d are invalid. The letter "f" is not used to designate orbitals, and the numbers in the designation should follow a specific order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, etc.
The orbital designation "4p 3s 2d 5f" is invalid because it does not follow the proper order of filling orbitals according to the Aufbau principle. The correct order is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, and 7p.
The Fermi wave vector expressions in 1D, 2D, and 3D are given by: 1D: k_F = (3π^2n)^(1/3) 2D: k_F = (πn)^(1/2) 3D: k_F = (3π^2n)^(1/3)
because its energy level is lower
An excited electron from the 3p orbital would most likely jump to the 4s orbital due to its lower energy level compared to the 3d orbital.
The filling order is determined by the Aufbau principle, which states that orbitals are filled in order of increasing energy. In the case of chromium, the 4s orbital is actually higher in energy than the 3d orbital due to electron-electron repulsions. This means that the 4s orbital is filled before the 3d orbital according to the n + l rule, which states that orbitals with lower values of n + l are filled first.