Question

According to Bohr’s model of hydrogen atom, the radius of a stationary orbit characterized by the principal quantum number n is proportional to:
A) ${{n}^{-1}}$
B) n
C) ${{n}^{-2}}$
D) ${{n}^{2}}$

Answer 1

Hint: Bohr model is also called Rutherford-bohr model. Bohr model is a system which consists of small dense nuclei surrounded by orbiting electrons. New quantum physical interpretation is mainly concerned in the Rutherford model or Rutherford-bohr model. The Bohr model was presented by Niels bohr and Ernest Rutherford.

Complete step-by-step solution:
The Bohr model is used to describe the structure of energy levels of hydrogen. Each shell is associated with principal quantum number n. The amount of energy in each cell is represented in electron volt(eV).ionization energy of 13.598eV is the maximum energy.

The above diagram represents the energy levels of hydrogen atom
Limitations of the Bohr model
 When larger atoms are used poor spectral predictions are obtained
In the Bohr model electrons with known radius and orbit are considered. Which violates the Heisenberg uncertainty principle.
Bohr models cannot predict the relative intensities of spectral lines.
 According to bohr model of hydrogen atom the radius of stationary orbit characterized by the principal quantum number n is proportional to \[{{n}^{2}}\].
So the correct option is D.
Note: Students atomic number is also called as proton number and mass number (A) of an atom is the addition of atomic number (Z) and number of neutrons (N).Atomic number is equal to number of electrons in uncharged atoms. The Bohr model will not explain the Zeeman effect and bohr model is very limited(in terms of size).