Bohr's model can be used for hydrogen-like ions—ions that have only one electron, such as He + and Li 2+ . (a) Why is the Bohr model applicable to He + ions but not to neutral He atoms?

Hey everyone in this example, we need to determine which of the below statements is a true statement. At a glance for all of our answer choices. They're all in regards to the Bohr model and we should recall that the Bohr model is used for hydrogen like atoms or rather ions we should say. And in this case, what hydrogen like means is having at least one electron. So looking at statement A it says that the Bohr model is applicable to helium because it is a hydrogen like ion, we would recognize helium on our periodic table with the atomic number two. So we would recall that atomic number can be represented by the symbol Z. So we would say that Z equals two and so therefore we have two electrons in helium. So we would rule out choice A because it's not applicable to the Bohr model, it's not like helium or hydrogen. Sorry. So moving on to statement B, it says that the Bohr model is applicable to lithium because it's a hydrogen like ion. When we think of lithium on the periodic table, we would find it in group one A. And we would see that it has the atomic number or Z value equal to three, which would correspond to three electrons for the neutral atom lithium. And so because it does not have one electron like hydrogen, we would also rule out statement B because it's not a true statement, it's a false statement just like statement A. So moving on to statement see it says that the Bohr model is applicable to the lithium two plus carry on because it is a hydrogen like ion, we should recall that having a carry on charge means we lose that number of electrons. So because we have a two plus charge on this carry on from our three electrons in a neutral atom of lithium we would lose to. And so that would leave us with one electron, which is equivalent to the one electron in a hydrogen atom. And so because this is or this matches up with the one electron in a hydrogen atom. This would be a true statement. And so we can consider choice. See a good anti choice. Moving onto choice D. We have the Bohr model is only applicable to the hydrogen atom. We know that this is not true because it's applicable to any ion that is hydrogen like meaning it will have one electron. And so that means that choice C is the only true statement. So it's our final answer for this example. If you have any questions, please leave them down below. Otherwise, I will see everyone in the next practice video

Ch.6 - Electronic Structure of Atoms

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Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 94a

Chapter 6, Problem 94a

Bohr's model can be used for hydrogen-like ions—ions that have only one electron, such as He⁺ and Li²⁺. (a) Why is the Bohr model applicable to He⁺ ions but not to neutral He atoms?

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Understand the Bohr model: The Bohr model is specifically designed for systems where a single electron orbits a nucleus. It simplifies the electron-nucleus interaction by considering only one electron moving in a fixed orbit around the nucleus.

Recognize the electron configuration of He+ and neutral He: Helium (He) in its neutral state has two electrons. When it loses one electron, becoming He+, it has only one electron remaining.

Consider electron-electron interaction: In neutral helium, the presence of two electrons means that electron-electron repulsion must be considered, which complicates the system beyond what the Bohr model can accurately handle.

Apply the Bohr model to He+: Since He+ has only one electron, the system is simplified to a single electron orbiting the nucleus, similar to the hydrogen atom. This fits the conditions under which the Bohr model provides a good approximation.

Conclude why Bohr model is not applicable to neutral He: The Bohr model does not account for interactions between multiple electrons, which is necessary for accurately describing the behavior of neutral helium with its two electrons.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Bohr's Model of the Atom

Bohr's model describes the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits. It quantizes the angular momentum of electrons, allowing only certain stable orbits. This model is particularly effective for hydrogen-like ions, where a single electron is influenced by the nucleus's charge.

Hydrogen-like Ions

Hydrogen-like ions are ions that contain only one electron, similar to hydrogen. Examples include He+ and Li2+. The simplicity of having a single electron allows for the application of Bohr's model, as the electron's behavior can be accurately predicted by the model's equations, unlike in multi-electron systems.

Electron-Electron Interactions

In neutral helium (He), there are two electrons that repel each other due to their negative charges. This electron-electron interaction complicates the energy levels and orbital shapes, making the Bohr model inadequate. The model does not account for these interactions, which are significant in multi-electron atoms, leading to deviations from the predictions made for hydrogen-like ions.

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Determine whether each of the following sets of quantum numbers for the hydrogen atom are valid. If a set is not valid, indicate which of the quantum numbers has a value that is not valid: (a) n = 3, l = 3, m_l = 2, m_s = +1/2 (b) n = 4, l = 3, m_l = -3, m_s = +1/2 (c) n = 3, l = 1, m_l = 2, m_s = +1/2 (d) n = 5, l = 0, m_l = 0, m_s = 0 (e) n = 2, l = 1, m_l = 1, m_s = -1/2

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Bohr's model can be used for hydrogen-like ions—ions that have only one electron, such as He+ and Li2+. (a) Why is the Bohr model applicable to He+ ions but not to neutral He atoms?

Verified Solution

Key Concepts

Bohr's Model of the Atom

Hydrogen-like Ions

Electron-Electron Interactions

Bohr's model can be used for hydrogen-like ions—ions that have only one electron, such as He⁺ and Li²⁺. (a) Why is the Bohr model applicable to He⁺ ions but not to neutral He atoms?