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The magnetization is composed of the sum of dipole moments associated with individual spins: $$\vec{M}=\sum_i \vec{\mu}_i$$ and the component along the magnetizing field (assumed to lie along the z axis) is \begin{align}M_z&= \left( \sum_i \vec{\mu}_i\right)_z \\ &= \sum_i \mu_{iz}\end{align} Since the individual dipole moment components ...
You are correct that a given value of $m_I$ and $I$ does correspond to one single value of the angle $\theta$. For the most commonly used nuclei in NMR spectroscopy, the "allowed" values are $I = 1/2$ and $m_I = \pm 1/2$. The two states are commonly labelled $\alpha$ and $\beta$; these are the eigenstates of the angular momentum projection operator $\hat{I}... 1 TL;DR: It's complicated and likely has to do with paramagnetic shielding effects rather than the usual arguments based on electron density, ring currents, and so on. Firstly, because of low-lying π* orbitals, π-bonded carbons typically have lower excitation energies than purely σ-bonded carbons and are thus more deshielded. However, due to the presence ... 0 The nitrile is sp hybridized while the carbonyl is sp2 hybridized, meaning that the orbitals around the nitrile carbon have more s character, leading to more shielding. 4 "How can it remain secret?". Trivial answer is - it can't (it isn't). WD40 is a Fast Moving Consumer Good (FMCG). It is also a reasonably cheap product - as an industrial chemist this suggests at least two things to me: It doesn't contain anything rare or expensive It isn't difficult to manufacture As an ex-petroleum chemical analyst, with access to a ... 5 when I was in school, I was told that [...] each pair of [equivalent] protons gives a doublet This is only strictly true for magnetically equivalent protons. If there is magnetic inequivalence, such as in the p-disubstituted benzene ring, then it is no longer true. It's not as simple as a dd either; when you have magnetically inequivalent protons that see ... 3 The two protons Hb and Hc are also chemically inequivalent, because they have a different chemical environment with the methyl group, i.e. they don´t have the same chemical shift. In a chiral molecule, the protons in a methylene group are rarely really chemically equivalent. There is usually a preferred orientation. 4 Seems to me there is an error in the last line of this list: No$\ce{^{195}Pt}$resulting in a singlet: intensity$0.66 \times 0.66$One$\ce{^{195}Pt}$resulting in a doublet: intensity$2 \times 0.66 \times 0.33$Two$\ce{^{195}Pt}$resulting in a singlet: intensity$0.33 \times 0.33\$ This results in a final ratio of 1:8:18:8:1 Simultaneous ...