Bohr Model of Hydrogen Atom

The Bohr model of the hydrogen atom was proposed by Danish physicist Niels Bohr in 1913. It was the first successful attempt to explain the electronic structure of an atom. According to this model, the electrons in an atom can occupy only certain fixed energy levels or stationary orbits around the nucleus.

Principal Quantum Number

The principal quantum number (n) is a positive integer that determines the energy level of an electron in an atom. The energy of an electron in a hydrogen atom is given by the equation:

E = -13.6/n^2 eV

where E is the energy of the electron, n is the principal quantum number, and -13.6 eV is the energy of the electron in the ground state (n=1).

Radius of Stationary Orbit

The radius of a stationary orbit around the nucleus of a hydrogen atom is given by the equation:

r = n^2 a0/ Z

where r is the radius of the orbit, n is the principal quantum number, a0 is the Bohr radius (0.529 Å), and Z is the atomic number (1 for hydrogen).

Proportional to n^2

From the above equation, we can see that the radius of a stationary orbit is proportional to n^2. This means that as the principal quantum number increases, the radius of the orbit increases.

Explanation

The principal quantum number determines the energy level of an electron in an atom. As the energy level increases, the electron is farther away from the nucleus and the radius of its orbit increases. Since the radius of the orbit is proportional to n^2, we can say that the radius increases exponentially as the value of n increases.

Conclusion

In conclusion, according to the Bohr model of the hydrogen atom, the radius of a stationary orbit characterized by the principal quantum number n is proportional to n^2. This means that as the value of n increases, the radius of the orbit increases exponentially.