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Chapter 7: Problem 47

Describe the four quantum numbers used to characterize an electron in an atom.

Short Answer

Expert verified
The four quantum numbers used to characterize an electron in an atom include the Principal Quantum Number (n), which signifies the size and energy level of an orbital; the Azimuthal Quantum Number (l), which denotes the shape of the orbital; the Magnetic Quantum Number (m), which represents the orientation of the orbital around the nucleus; and the Spin Quantum Number (s), that determines the orientation of the electron's spin.

Step by step solution

01

Principal Quantum Number (n)

The Principal Quantum Number, denoted by 'n', is the first quantum number and it corresponds to the size and energy level of the orbital. The greater the 'n', the higher the energy level and the larger the orbital. It can have any positive integer value.
02

Azimuthal Quantum Number (l)

The Azimuthal Quantum Number, denoted by 'l', also known as the angular momentum quantum number, helps in defining the shape of the orbital. It can have any integer value from 0 to \(n-1\). For a given 'l', \(2l + 1\) magnetic quantum numbers exist corresponding to different orientations.
03

Magnetic Quantum Number (m)

The Magnetic Quantum Number, denoted by 'm', describes the orientation of the orbital around the nucleus. It can take values ranging from \(-l\) through 0 to \(+l\).
04

Spin Quantum Number (s)

The Spin Quantum Number, denoted by 's', determines the orientation of the electron's spin and can have two possible values: \(+0.5\) (spin-up) and \(-0.5\) (spin-down).

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Most popular questions from this chapter

In an electron microscope, electrons are accelerated by passing them through a voltage difference. The kinetic energy thus acquired by the electrons is equal to the voltage times the charge on the electron. Thus, a voltage difference of \(1 \mathrm{~V}\) imparts a kinetic energy of \(1.602 \times 10^{-19} \mathrm{C} \times \mathrm{V}\) or \(1.602 \times\) \(10^{-19} \mathrm{~J}\). Calculate the wavelength associated with electrons accelerated by \(5.00 \times 10^{3} \mathrm{~V}\).

(a) If a \(\mathrm{H}\) atom and a He atom are traveling at the same speed, what will be the relative wavelengths of the two atoms? (b) If a \(\mathrm{H}\) atom and a He atom have the same kinetic energy, what will be the relative wavelengths of the two atoms?

Identify the following individuals and their contributions to the development of quantum theory: Bohr, de Broglie, Einstein, Planck, Heisenberg, Schrödinger.

A laser is used in treating retina detachment. The wavelength of the laser beam is \(514 \mathrm{nm}\) and the power is \(1.6 \mathrm{~W}\). If the laser is turned on for \(0.060 \mathrm{~s}\) during surgery, calculate the number of photons emitted by the laser. \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\)

Owls have good night vision because their eyes can detect a light intensity as low as \(5.0 \times 10^{-13} \mathrm{~W} / \mathrm{m}^{2}\). Calculate the number of photons per second that an owl's eye can detect if its pupil has a diameter of \(9.0 \mathrm{~mm}\) and the light has a wavelength of \(500 \mathrm{nm}\) \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\)
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