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Chapter 8: Problem 57

Select the correct answer and explain your reasoning. An electron having \(n=3\) and \(m_{\ell}=0\) (a) must have \(m_{s}=+\frac{1}{2} ;(\mathbf{b})\) must have \(\ell=1 ;(\mathbf{c})\) may have \(\ell=0,1\) or \(2 ;\) (d) must have \(\ell=2\).

Short Answer

Expert verified
The correct option is (c), because when \(n=3\), the electron can have \(\ell=0,1\) or \(2\).

Step by step solution

01

Analyze Option A

Option (a) refers to the spin quantum number \(m_{s}\). It does not depend on either \(n\) or \(m_{\ell}\), so we can't say it must have \(m_{s}=+\frac{1}{2}\). It can have either \(+\frac{1}{2}\) or \(-\frac{1}{2}\). Therefore, option (a) is incorrect.
02

Analyze Option B

Option (b) states the electron must have \(\ell=1\). However, since \(n=3\), the value of \(\ell\) can range from 0 to 2. Therefore, it doesn't have to be that \(\ell=1\). So, option (b) is also incorrect.
03

Analyze Option C

Option (c) suggests the electron may have \(\ell=0,1\) or \(2\). This is logically correct because for \(n=3\), the possible values of \(\ell\) can indeed range from 0 to 2. Therefore, option (c) is correct. Nevertheless, we should analyze option (d) to complete our examination.
04

Analyze Option D

Option (d) states that the electron must have \(\ell=2\). However, as in option (b), we have already established that the value of \(\ell\) can range from 0 to 2 for \(n=3\). So, option (d) is incorrect.

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Most popular questions from this chapter

The following electron configurations correspond to the ground states of certain elements. Name each element. (a) \([\mathrm{Rn}] 7 s^{2} 6 d^{2} ;\) (b) \([\mathrm{He}] 2 s^{2} 2 p^{2} ;\) (c) \([\mathrm{Ar}] 3 d^{3} 4 s^{2}\) (d) \([\mathrm{Kr}] 4 d^{10} 5 s^{2} 5 p^{4} ;\) (e) \([\mathrm{Xe}] 4 f^{2} 6 s^{2} 6 p^{1}\)

The magnesium spectrum has a line at \(266.8 \mathrm{nm}\). Which of these statements about this radiation is (are) correct? Explain. (a) It has a higher frequency than radiation with wavelength \(402 \mathrm{nm}\) (b) It is visible to the eye. (c) It has a greater speed in a vacuum than does red light of wavelength \(652 \mathrm{nm}\) (d) Its wavelength is longer than that of X-rays.

What is \(\Delta E\) for the transition of an electron from \(n=6\) to \(n=3\) in a Bohr hydrogen atom? What is the frequency of the spectral line produced?

Without doing detailed calculations, determine which of the following wavelengths represents light of the highest frequency: (a) \(6.7 \times 10^{-4} \mathrm{cm} ;\) (b) \(1.23 \mathrm{mm}\) (c) \(80 \mathrm{nm} ;\) (d) \(6.72 \mu \mathrm{m}\)

Although Einstein made some early contributions to quantum theory, he was never able to accept the Heisenberg uncertainty principle. He stated, "God does not play dice with the Universe." What do you suppose Einstein meant by this remark? In reply to Einstein's remark, Niels Bohr is supposed to have said, "Albert, stop telling God what to do." What do you suppose Bohr meant by this remark?
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