To determine the atomic number of the element, we need to understand the meaning of the given quantum numbers.

The quantum number n represents the principal energy level or shell of the electron. In this case, n = 3, indicating that the electron is in the third energy level.

The quantum number l represents the azimuthal or orbital angular momentum quantum number. It determines the shape of the orbital. Here, l = 2, which corresponds to the d orbital.

The quantum number m represents the magnetic quantum number. It specifies the orientation of the orbital in space. The value m = +2 indicates that the electron is in the d orbital with an orientation of +2.

The quantum number s represents the spin quantum number. It describes the spin of the electron. The value s = +1/2 indicates that the electron has a spin of +1/2.

Now, we can determine the atomic number of the element. The atomic number is equal to the number of protons in the nucleus of an atom. In a neutral atom, the number of electrons is also equal to the atomic number.

Since the electron in question is the last entering electron, it will occupy the highest energy level available. In this case, it is the third energy level (n = 3).

The maximum number of electrons that can be accommodated in the third energy level is given by the formula 2n^2. For n = 3, the maximum number of electrons is 2(3)^2 = 18.

To determine the atomic number, we need to find the position of the electron in the electron configuration. The electron configuration for the given quantum numbers is 3d^2.

The atomic number is equal to the number of electrons, so the atomic number of the element will be the number of electrons in the 3d orbital, which is 2.

Therefore, the correct answer is (a) 13, as it is the only option that corresponds to an atomic number of 13.

Question

To determine the atomic number of the element, we need to understand the meaning of the given quantum numbers.

The quantum number n represents the principal energy level or shell of the electron. In this case, n = 3, indicating that the electron is in the third energy level.

The quantum number l represents the azimuthal or orbital angular momentum quantum number. It determines the shape of the orbital. Here, l = 2, which corresponds to the d orbital.

The quantum number m represents the magnetic quantum number. It specifies the orientation of the orbital in space. The value m = +2 indicates that the electron is in the d orbital with an orientation of +2.

The quantum number s represents the spin quantum number. It describes the spin of the electron. The value s = +1/2 indicates that the electron has a spin of +1/2.

Now, we can determine the atomic number of the element. The atomic number is equal to the number of protons in the nucleus of an atom. In a neutral atom, the number of electrons is also equal to the atomic number.

Since the electron in question is the last entering electron, it will occupy the highest energy level available. In this case, it is the third energy level (n = 3).

The maximum number of electrons that can be accommodated in the third energy level is given by the formula 2n^2. For n = 3, the maximum number of electrons is 2(3)^2 = 18.

To determine the atomic number, we need to find the position of the electron in the electron configuration. The electron configuration for the given quantum numbers is 3d^2.

The atomic number is equal to the number of electrons, so the atomic number of the element will be the number of electrons in the 3d orbital, which is 2.

Therefore, the correct answer is (a) 13, as it is the only option that corresponds to an atomic number of 13.

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