Bohr Model Of The Hydrogen Atom

Step 1: Understanding the Bohr magneton.
The Bohr magneton is the magnetic moment of an electron in a hydrogen atom. It is given by the formula: where is the charge of the electron, is the reduced Planck constant, and is the mass of the electron.
Step 2: Conclusion.
The formula for the Bohr magneton is .

Step 1: Radius of electron orbit.
The radius of the -th orbit in the hydrogen atom is given by: where is the radius of the first orbit and is the orbit number.
Step 2: Comparing the radius for the 8th and 4th orbits.
For the 8th orbit, the radius is . For the 4th orbit, the radius is . The ratio of the radii is:
Step 3: Conclusion.
The radius of the eighth orbit is more than that of the fourth orbit by a factor of 8, corresponding to option (3).

Step 1: Stationary Orbits.
In Bohr’s model, electrons are restricted to certain fixed orbits or energy levels around the nucleus. These orbits do not radiate energy despite the motion of the electron.
Step 2: Quantization of Angular Momentum.
Bohr postulated that the angular momentum of an electron in these stable orbits is quantized and given by: where is a positive integer (quantum number), and is the reduced Planck’s constant.
Step 3: Emission and Absorption of Radiation.
When an electron jumps from a higher orbit to a lower one, it emits radiation with energy . Similarly, when an electron absorbs energy, it moves to a higher orbit.
Step 4: Conclusion.
Bohr’s postulates explain the discrete nature of electron energy levels and the emission or absorption of radiation in discrete quantities.