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Chapter 7: Problem 54

An electron in an atom is in the \(n=3\) quantum level. List the possible values of \(\ell\) and \(m_{\ell}\) that it can have.

Short Answer

Expert verified
For the third quantum level (\(n = 3\)), the possible combinations of \(\ell\) and \(m_{\ell}\) are: (\(0, 0\)), (\(1, -1\)), (\(1, 0\)), (\(1, 1\)), (\(2, -2\)), (\(2, -1\)), (\(2, 0\)), (\(2, 1\)), (\(2, 2\)).

Step by step solution

01

Determine the possible values of \(\ell\)

The azimuthal quantum number \(\ell\) can have integer values ranging from 0 to \(n-1\). Here, with \(n = 3\), the possible values of \(\ell\) can be 0, 1, or 2.
02

Determine the possible values of \(m_{\ell}\) for each \(\ell\)

For each value of \(\ell\), \(m_{\ell}\) can have integer values ranging from \(-\ell\) to \(\ell\). Consequently, when \(\ell = 0\), \(m_{\ell} = 0\); when \(\ell = 1\), \(m_{\ell}\) can be \(-1, 0, 1\); and when \(\ell = 2\), \(m_{\ell}\) can be \(-2, -1, 0, 1, 2\).

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Most popular questions from this chapter

An electron in a hydrogen atom is excited from the ground state to the \(n=4\) state. Comment on the correctness of the following statements (true or false). (a) \(n=4\) is the first excited state. (b) It takes more energy to ionize (remove) the electron from \(n=4\) than from the ground state. (c) The electron is farther from the nucleus (on average) in \(n=4\) than from the ground state. (d) The wavelength of light emitted when the electron drops from \(n=4\) to \(n=1\) is longer than that from \(n=4\) to \(n=2\). (e) The wavelength the atom absorbs in going from \(n=1\) to \(n=4\) is the same as that emitted as it goes from \(n=4\) to \(n=1\).

Give the high and low wavelength values that define the visible region of the electromagnetic spectrum.

Calculate the total number of electrons that can occupy (a) one \(s\) orbital, (b) three \(p\) orbitals, (c) five \(d\) orbitals, (d) seven \(f\) orbitals.

Does a baseball in flight possess wave properties? If so, why can we not determine its wave properties?

(a) What is the wavelength (in nanometers) of light having a frequency of \(8.6 \times 10^{13} \mathrm{~Hz} ?\) (b) What is the frequency (in Hz) of light having a wavelength of \(566 \mathrm{nm} ?\)
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