📘 Question:
The equation: 2πr = nλ
means that the path of the electron must have a length of an integral number of wavelengths, if not the wave will destruct.
→ True or False?
The equation: 2πr = nλ
means that the path of the electron must have a length of an integral number of wavelengths, if not the wave will destruct.
→ True or False?
✅ Answer: True
The equation 2πr = nλ is derived from Bohr’s atomic model, describing allowed orbits of electrons in a hydrogen atom.
- r = radius of orbit
- λ = de Broglie wavelength
- n = principal quantum number (n = 1, 2, 3…)
This means that the circumference of the orbit must be an exact multiple of the wavelength: nλ. Only then will the electron wave reinforce itself through constructive interference.
If this condition is not met, the electron wave will interfere destructively with itself, making the orbit unstable.
Hence, this quantization condition is necessary to ensure that the electron can exist in a stable orbit around the nucleus.