Question

What is the maximum number of electrons in an atom that can have these quantum numbers?

A. n=4
B. n=5; ml=+1
C. n=5; ms= +1/2
D. n=3; l=2; ml=-1
E. n=2; l=1

Answer 1

inal Answer:

The maximum number of electrons in an atom with the specified quantum numbers is determined by the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers. Therefore, the answer can be calculated as 2(2l + 1).

A. n=4 → Maximum electrons = 2(2(4) + 1) = 18 electrons.

Step-by-step explanation:

The Pauli Exclusion Principle plays a crucial role in determining the maximum number of electrons that can occupy a set of quantum numbers. For option A, where n=4, the maximum number of electrons is calculated using the formula 2(2l + 1), where l is the azimuthal quantum number. In this case, for n=4, the maximum electrons would be 2(2(4) + 1) = 18 electrons. This accounts for the various possible combinations of magnetic quantum number (ml) and spin quantum number (ms) within the given principal quantum number.

Each set of quantum numbers defines a unique electron state, and the Pauli Exclusion Principle ensures that no two electrons within an atom can have the same set of quantum numbers. Therefore, the formula 2(2l + 1) helps calculate the maximum number of electrons for a given value of n and l.

In summary, applying the Pauli Exclusion Principle and the formula 2(2l + 1) to the specified quantum numbers in each option allows us to determine the maximum number of electrons that can occupy the respective electron states in an atom.

Answer 2

The maximum number of electrons with the given quantum numbers are:

A. n=4 ➝ Maximum electrons = 32

B. n=5; ml=+1 ➝ Maximum electrons = 2

C. n=5; ms= +1/2 ➝ Maximum electrons = 50

D. n=3; l=2; ml=-1 ➝ Maximum electrons = 10

E. n=2; l=1 ➝ Maximum electrons = 4

Step-by-step explanation:

A. For n=4, the maximum number of electrons in the fourth energy level (n=4) is determine 2n²

which equals 2 ×4² = 2 ×16 = 32.

B. When n=5 and ml=+1, this specifies the orientation of the orbital in a subshell. Since ml can take values from -l to +l, and l corresponds to the azimuthal quantum number (l), the maximum number of electrons for ml=+1 in a subshell is 2.

C. With n=5 and ms=+1/2, this specifies the electron's spin in an orbital. The maximum number of electrons in a given orbital is 2, as electrons have two spin states: +1/2 and -1/2. Therefore, the maximum number of electrons with these quantum numbers is 2 * 25 = 50.

D. For n=3, l=2, and ml=-1, this indicates the orientation of the orbital in a subshell. With l=2, ml can take values -2, -1, 0, 1, 2, giving 5 orientations. Each orientation can hold a maximum of 2 electrons, so 5 * 2 = 10 electrons.

E. For n=2 and l=1, this specifies a p-orbital within the second energy level. A p-orbital has three orientations (ml values of -1, 0, 1) and can accommodate a total of 6 electrons (2 electrons per orientation). However, the question only specifies ml=-1, so the maximum number of electrons for this particular ml value is 2.

In summary, the quantum numbers define the energy levels, subshells, orientations, and spin states of electrons in an atom, enabling us to calculate the maximum number of electrons that can occupy specific quantum states within an atom's structure.