Question

One electron is in the n=3 state of a molecule with a bond of length 0.13 nm, and another electron is in the n=3 state of a molecule with a bond of length 0.15 nm. What is the energy difference between the two states? Give your answer in eV to 1 decimal place. Do NOT include units in your answer and do NOT correct for the bond angles.

Answer 1

The energy difference between two electrons both in the n=3 state of molecules with different bond lengths is 0 eV, as energy levels are determined by the quantum number and not bond length in this context.

Step-by-step explanation:

To calculate the energy difference between two electron states in different molecules, we apply the formula En = (-13.6 eV/n²) for the energy levels of an electron in a hydrogen-like atom, where n is the principal quantum number.

For both electrons in the n=3 state, the energy is calculated as:

E = -13.6 eV / 3² = -13.6 eV / 9

E = -1.5111... eV

This energy value is constant for a given n and does not depend on the bond length. Because both electrons are in the same quantum state, n=3, and the question asks us to ignore bond angles and only consider the energy levels, the energy difference between the two states is 0 eV. The bond length does not affect the energy of a specific quantum state in this scenario.