Question

Use the Bohr model to calculate the radius, in angstroms, of an Li2+ ion with an electron in the 𝑛=5 state.

Answer 1

[AI-generated answer — Explain Bot]

To calculate the radius of an Li2+ ion with an electron in the 𝑛=5 state using the Bohr model, we need to consider a few important principles.

1. The Bohr model states that electrons orbit the nucleus in discrete energy levels or shells.
2. The radius of each energy level is given by the Bohr radius (𝑎₀), which is approximately equal to 0.529 Å (angstroms).

Now, let's calculate the radius step by step:

1. Determine the principal quantum number (𝑛) for the energy level of interest. In this case, 𝑛=5.

2. Use the formula for calculating the radius of an electron orbit in the Bohr model:

𝑟 = 𝑛² × 𝑎₀

where 𝑟 is the radius of the orbit, 𝑛 is the principal quantum number, and 𝑎₀ is the Bohr radius.

Plugging in the values, we have:

𝑟 = 5² × 0.529 Å

Simplifying further, we get:

𝑟 = 25 × 0.529 Å

𝑟 = 13.225 Å

So, the radius of the Li2+ ion with an electron in the 𝑛=5 state is approximately 13.225 angstroms.