Which of the following statements is true regarding the allowed energies of a quantum system with energy levels at 1.0 eV, 2.0 eV, 4.0 eV, and 7.0 eV?

• A. A transition from 4.0 eV to 1.0 eV releases 2.0 eV of energy.
• B. The lowest possible energy of the system is 0.0 eV.
• C. The energy difference between every adjacent level is the same.
• D. A transition from 2.0 eV to 4.0 eV requires the absorption of 2.0 eV of energy.

Answer: (D)

Verified step by step guidance

1. Identify the given energy levels of the quantum system: 1.0 eV, 2.0 eV, 4.0 eV, and 7.0 eV.
2. Recall that the energy difference between two levels corresponds to the energy absorbed or released during a transition: \(\Delta E = E_{final} - E_{initial}\).
3. Check each statement by calculating the energy differences involved: for example, from 4.0 eV to 1.0 eV, \(\Delta E = 1.0 - 4.0 = -3.0\) eV, which means 3.0 eV is released, not 2.0 eV.
4. Verify if the lowest possible energy is 0.0 eV by examining the given levels; since the lowest level is 1.0 eV, 0.0 eV is not an allowed energy state here.
5. Compare energy differences between adjacent levels: between 1.0 and 2.0 eV is 1.0 eV, between 2.0 and 4.0 eV is 2.0 eV, and between 4.0 and 7.0 eV is 3.0 eV, so they are not equal, confirming that the energy gaps are not uniform.