A GOOD QUESTION ON BOHR'S THEORY...TRY IT....

The quantum number of

of the state finally populated in He+ ions is

n A.)2 B.) 3 C.) 4 D.) 5

To determine the quantum number of the state finally populated in He⁺ ions, we first need to understand a few key concepts about atomic structure and the Bohr model. The Bohr model, while primarily applicable to hydrogen-like atoms, can also be adapted to understand ions like He⁺, which has only one electron. This makes it similar to hydrogen, but with a different nuclear charge.

Understanding He⁺ Ions

Helium has two protons in its nucleus, giving it a nuclear charge of +2. When it loses one electron to become He⁺, it behaves like a hydrogen atom but with a stronger attraction between the nucleus and the remaining electron due to the increased positive charge.

Bohr's Model and Quantum Numbers

In the Bohr model, the energy levels of an electron in a hydrogen-like atom are given by the formula:

• E_n = - (Z² * 13.6 eV) / n²

Here, Z is the atomic number (which is 2 for helium), and n is the principal quantum number, which can take positive integer values (1, 2, 3, ...). The energy levels become less negative (higher energy) as n increases.

Finding the Quantum Number

Now, let’s consider the question about the final populated state. In a typical scenario, when an electron transitions between energy levels, it can absorb or emit energy in the form of photons. For He⁺, the electron will occupy the lowest available energy state first, which corresponds to the lowest quantum number.

For He⁺, the ground state corresponds to n = 1. However, if we are looking for a specific excited state or a transition, we need to consider the options provided:

• A) 2
• B) 3
• C) 4
• D) 5

In many cases, the question might imply that we are looking for the first excited state, which would be n = 2. This is the first energy level above the ground state where the electron can reside after absorbing energy.

Conclusion on the Quantum Number

Given the options and the context of the question, the most logical choice for the quantum number of the state finally populated in He⁺ ions is A) 2. This indicates that the electron has moved from the ground state (n=1) to the first excited state (n=2) after absorbing energy.

In summary, understanding the behavior of electrons in ions like He⁺ through the lens of Bohr's theory allows us to predict the quantum states they can occupy based on their energy levels. This foundational knowledge is crucial for deeper explorations into atomic physics and quantum mechanics.