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Chapter 3: Problem 76

How many quantum numbers are needed to identify an electron in an atom?

Short Answer

Expert verified
Answer: A total of four quantum numbers (n, l, m_l, m_s) are needed to uniquely identify an electron in an atom. They provide information about the electron's energy level, orbital shape, orbital orientation, and spin.

Step by step solution

01

Understanding Quantum Numbers

Quantum numbers are a set of numerical values that help describe the characteristics and position of an electron within an atom. They give information about the energy level, shape, orientation, and spin of an electron's orbital. In total, there are four quantum numbers that are needed to define an electron's position in an atom.
02

Describing Principal Quantum Number (n)

The first quantum number is called the principal quantum number and is denoted by "n". It is a positive integer (n = 1, 2, 3, ...) and represents the energy level (or shell) in which the electron resides. As the value of n increases, the distance of the electron from the nucleus also increases, meaning the electron is less tightly bound to the nucleus.
03

Describing Azimuthal Quantum Number (l)

The second quantum number is the azimuthal quantum number, represented by "l". This number describes the shape and type of an electron's orbital, and it has integer values ranging from 0 to (n-1). The different types of orbitals are denoted by letters s, p, d, f, where l=0 corresponds to s, l=1 is p, l=2 is d, and l=3 is f.
04

Describing Magnetic Quantum Number (m_l)

The third quantum number is the magnetic quantum number, denoted as "m_l". It describes the orientation of the orbital in space. The value of m_l ranges from -l to +l, including zero. This means that an orbital with an azimuthal quantum number l will have (2*l + 1) different orientations in space.
05

Describing Spin Quantum Number (m_s)

The fourth and final quantum number is the spin quantum number, represented by "m_s". It describes the intrinsic angular momentum or spin of the electron. Electrons, being fermions, have spin values of 卤1/2. This means that for any given electron, m_s can either be +1/2 (spin-up) or -1/2 (spin-down).
06

Conclusion

In conclusion, a total of four quantum numbers (n, l, m_l, m_s) are needed to uniquely identify an electron in an atom. These quantum numbers provide information about the electron's energy level, orbital shape, orbital orientation, and spin.

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Most popular questions from this chapter

Identify the subshells with the following combinations of quantum numbers and arrange them in order of increasing energy in a multielectron atom: a. \(n=3, \ell=2\) b. \(n=7, \ell=3\) c. \(n=3, \ell=0\) d. \(n=4, \ell=1\)

How does the wavelength of light required to ionize a gasphase atom change with increasing atomic number down a group in the periodic table?

How does the concept of an orbit in the Bohr model of the hydrogen atom differ from the concept of an orbital in quantum theory?

Without referring to Figure \(3.37,\) arrange the following groups of elements in order of increasing first ionization energy. a. \(\mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}\) b. \(\mathrm{He}, \mathrm{Ne}, \mathrm{Ar}, \mathrm{Kr}\) c. \(\mathrm{P}, \mathrm{S}, \mathrm{Cl}, \mathrm{Ar}\)

An electron affinity (EA) value that is negative indicates that the free atoms of an element are higher in energy than the \(1-\) anions they form by acquiring electrons. Does this mean that all of the elements with negative EA values exist in nature as anions? Give some examples to support your answer.
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