Which of the following is an assumption made by Bohr about the hydrogen atom?

• A. Electrons can exist anywhere around the nucleus with any energy value.
• B. Electrons move in fixed circular orbits around the nucleus without radiating energy.
• C. The nucleus contains both protons and neutrons.
• D. Electrons are stationary and do not move around the nucleus.

Answer: (B)

Verified step by step guidance

1. Understand that Bohr's model of the hydrogen atom was developed to explain atomic spectra and stability of atoms, which classical physics could not adequately describe.
2. Recall that Bohr proposed electrons move in specific, fixed circular orbits around the nucleus, each orbit corresponding to a quantized energy level.
3. Recognize that in these fixed orbits, electrons do not emit energy as radiation, which prevents the electron from spiraling into the nucleus—a key assumption to explain atomic stability.
4. Note that Bohr's model assumes quantization of angular momentum, meaning the electron's angular momentum is an integer multiple of \(\hbar = \frac{h}{2\pi}\), where \(h\) is Planck's constant.
5. Identify that the other options either contradict Bohr's assumptions (such as electrons being stationary or the nucleus composition) or reflect classical ideas that Bohr's model replaced.