In an atom of barium, how many electrons have l = 0 and ml = 1.

L refers to the subshell, and L=0 goes with the S-subshell. since Ba is in the 6th shell, there would be 12 electrons in the S-subshell. as for ml values, they rage from -L to L, and since your L value is 0, the only ml value you have is 0 and so there are no electrons that have both values of L=0 and ml=1.

12 electrons

Explanation:

As the electrons move around the atom, they can move in any direction as long as they stay in their shell, and they are also constantly spinning. Shells or orbitals are specific distances from the nucleus and they are energy levels. Each of those shells has a name and there are a many ways that atomic shells are described.

First, the basic regions where electrons are found which is described using an "n" value, or the letters K, L, M, N, O, P, and Q. The "K" shell is the one closest to the nucleus, and "Q" is the farthest away. The second description looks at how electrons act inside of the shells, described with the "l" value which indicates in which suborbital an electron is found in (s, p, d, f, g, and h)

Quantum numbers are numbers associated with physical quantities conserved in certain quantum systems. 

The main quantum number n This quantum number is related to both energy and the average distance between the nucleus and the electron. The values of this number, which corresponds to the number of the energy level, vary theoretically between 1 and infinity, but only atoms are known that have up to 8 energy levels in their fundamental state since the atomic number and the main quantum number are related by 2n2 = Z < 110.The secondary quantum number is L (l = 0,1,2,3,4,5,...,n-1), it indicates the shape of the orbitals and the sublevel of energy in which the electron is found. l = 0: Suborbit "s" (circular shape), it has a space for two electrons. l = 1: Suborbit "p" (flattened semicircular shape), it has three spaces for six electrons. l = 2: Sub-orbit "d" (lobular shape, with a nodal ring), it has five spaces for ten electrons. l = 3: Sub-orbit "f" (lobular with radial nodes), it has seven spaces for fourteen electrons. l = 4: Sub-orbit "g" (*), l = 5: Sub-orbit "h"The magnetic quantum number (m, ml), indicates the spatial orientation of the energy sublevel, "(m = -l,...,0,...,l)". For each value of l there are 2l+1 values of m.The spin quantum number (s, ms), Describes the intrinsic angular momentum of the electron. This angular momentum was originally interpreted in a classical way as the "self-rotation" of the electron on itself, and it was considered that given an axis the electron could do in two directions, opposite to each other. Therefore, the values that the spin quantum number can take are -1/2 and +1/2. In other words, each electron, in an orbit, spins on itself.

So, L refers to the s subshell, so L=0 is related with the S-subshell. Ba is an atom found in the 6th shell, and it has the electronic configuration of [Xe]6s2 (1s2s2p3s3p4s3d4p5s4d5p6s), so there would be .12 electrons there because there are 6 s-orbitals with 2 electrons each. On the other hand, ml values rage from -L to L, and since the L value from this question is 0, there are no electrons that have both values of L=0 and ml=1. Since only one orbital of each type can have this magnetic quantum number and each orbital can host 2 electrons, we also have 12 electrons fitting this description.  

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