Question

who are the quantum numbers n,l,m and s arrived at?explain the significance of quantum numbers?​

Answer 1

Answer:

Quantum numbers are a way to describe the discrete states that a particle can hold. These can then be used for solutions to the Schrodinger equation(above).

Principal Quantum Number (n)—this designates the size of the orbital, also called the shell. The larger the value for n, the greater the average distance of an electron in the orbital from the nucleus and therefore the larger the orbital. (I could always remember this trend by relating it back to Coulomb’s Law of Attractive Forces.) From the equation that defines the line spectrum of Hydrogen, we can also know that the value for n represents energy levels.

Angular Momentum Quantum Number (l)—this describes the shape of the orbital, but again, you can relate it back to the periodic table. The values of l are integers that depend on the value of the principal quantum number, n. For any given value of n, the possible range of values for l go from 0 to n−1. If n=1, there’s only one possible value of l; that is, 0 (n−1 where n=1). If n=2, there’s two values for l : 0 and 1. If n=3, l has three values: 0, 1, and 2.

Magnetic Quantum Number (ml)—this describes the orientation of the orbital in space, or the direction along the axes in which it faces. Within a sub-shell, the value of this depends on the value of l. For a certain value of l, there are (2l+1) integral values, or −l,…0,…+l

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Answer 2

The path and motion of an electron in an atom can be represented by quantum numbers.

• The Schrodinger equation must hold true for the total quantum numbers of all the electrons in a specific atom.
• Quantum numbers are the set of numbers used to express the location and energy of an electron in an atom.
• The primary, azimuthal, magnetic, and spin quantum numbers are the four types of quantum numbers.
• Quantum numbers provide the values of a quantum system's preserved quantities.
• The Schrodinger wave equation for hydrogen atoms has solutions provided by a set of numerical values known as electronic quantum numbers (the quantum numbers describing electrons).
• All the properties of a given electron in an atom can be fully described by the following four quantum numbers:

1. n stands for the principal quantum number.
2. The symbol for azimuthal quantum number (or orbital angular momentum quantum number) is l.
3. The symbol for a magnetic quantum number is $m_{l}$.
4. The $m_{s}$ symbol stands for the electron spin quantum number.

• According to Hund's laws, it is impossible for two electrons from the same atom to have the exact same quantum state or the exact values of the set of quantum numbers.
• The period of an atom is determined by the energy level, or n. The electron is further from the nucleus and has a higher energy with a higher n level.
• The square angular momentum of the electron in its orbital is determined by the quantum number l.
• The angular momentum projection along the z axis is determined by the m quantum number, which ranges from -l to l.
• Last but not least, the electron's spin, or intrinsic angular momentum independent of the orbit, is determined by the s quantum number.

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