Why are electrons restricted to certain energy levels in an atom?

• A. Because only specific energy values are allowed by the quantization of electron wavefunctions
• B. Because electrons can occupy any energy level without restriction
• C. Because electrons are attracted to the nucleus by gravitational forces
• D. Because the number of protons determines the allowed energy levels

Answer: (A)

Verified step by step guidance

1. Understand that electrons in an atom behave both as particles and waves, according to quantum mechanics.
2. Recognize that the electron's wavefunction must satisfy certain boundary conditions, meaning it can only exist in standing wave patterns around the nucleus.
3. These standing wave patterns correspond to specific, discrete energy levels, which is why electrons cannot have arbitrary energies.
4. This concept is known as quantization, where only certain energy values are allowed because the wavefunction must be stable and continuous.
5. Therefore, electrons are restricted to certain energy levels because only specific energy values satisfy the quantum mechanical conditions for their wavefunctions.