An atom it ground state contains 18 electrons. How many of these electrons are in orbitals with l=0? a.4 b.2 c.8 d.6

Make a table.

N.......1|..2.....|...3...........|
l.......0|..0..1..|...0....1.....2|
elec,,,,:|,,:|:::|,,,,:,,,:::,,,,,|
Count the electrons (: = 2 electrons) in l = 0. I count 16 total electrons of which there are 6 with l = 0

To determine the number of electrons in orbitals with l=0, we need to consider the quantum numbers associated with each electron.

The quantum number l represents the azimuthal or angular momentum quantum number. It determines the shape of the orbital and can have integer values ranging from 0 to n-1, where n is the principal quantum number.

In this case, the atom is in its ground state and contains 18 electrons. To find the number of electrons with l=0, we need to look at the values of n and l for each electron.

For the ground state, the principal quantum number n can be calculated using the formula:

n = 2 x k^2

where k is the shell number. In this case, we need to find the value of k for which 2k^2 is equal to or less than 18. By trying different values, we find that k=3 satisfies this condition.

Thus, the principal quantum number n for the ground state of this atom is:

n = 2 x 3^2 = 18

Next, we need to determine the values of l for each electron in the ground state. Since l can range from 0 to n-1, the possible values for l in this case are 0, 1, 2, ..., 17.

However, we are specifically interested in the number of electrons with l=0. Since l=0 corresponds to the s orbital, there is only one s orbital in each shell. Therefore, there can be only one electron with l=0 for each shell.

Since the principal quantum number n is 18 for this atom, it means that there are a total of 18 shells.

In each shell, there is only one electron with l=0. Therefore, the number of electrons in orbitals with l=0 would be equal to the number of shells.

In this case, there are 18 shells in the atom's ground state. Therefore, the number of electrons in orbitals with l=0 would be:

Answer: d. 6

To determine the number of electrons in orbitals with l = 0 in a ground state atom, we need to recall the rules for assigning electrons to orbitals.

The quantum number l describes the shape of the orbital. For l = 0, the orbital shape is s (spherical). Each s orbital can hold a maximum of 2 electrons.

In a ground state atom, we can use the Aufbau principle to determine the electron configuration. According to the Aufbau principle, electrons occupy the lowest energy orbitals available first.

Given that the atom in question has 18 electrons, we need to fill the orbitals in order of increasing energy until we have accounted for all the electrons.

The electron configuration for the first 18 electrons is as follows:
1s² 2s² 2p⁶ 3s² 3p⁶

Now, let's count how many electrons are in the orbitals with l = 0 (s orbitals). From the electron configuration, we can see that there are only 2 electrons in the 1s orbital.

Therefore, the answer is b. 2.