Answer:

Introduction:
The Hydrogen atom consists of a single proton and an electron revolving around it. It is one of the simplest atoms and was the first to be studied in detail, leading to the development of the Bohr model.

Statement:
For a Hydrogen atom, which one of the following statements is correct?

a) The radius of the orbits is an integral multiple of Bohr's radius (0.053 mm).
b) The angular momentum is n times h/2π.
c) The energy in the nth orbit is n times the ground state energy.
d) None of the above.

Explanation:

The Bohr Model:
The Bohr model is a simple model of the Hydrogen atom that was proposed by Niels Bohr in 1913. According to this model, the electron in a Hydrogen atom revolves around the nucleus in circular orbits. These orbits have a fixed radius and energy, and the electron can only occupy certain discrete energy levels.

Bohr's radius:
Bohr's radius is a physical constant that represents the most probable distance between the electron and the nucleus in a Hydrogen atom. Its value is 0.053 nm.

Angular momentum:
The angular momentum of an electron in a Hydrogen atom is given by the formula:

L = n h/2π

where n is the principal quantum number, h is Planck's constant, and π is the mathematical constant pi.

Energy levels:
The energy levels in a Hydrogen atom are given by the formula:

E = -13.6 eV/n^2

where n is the principal quantum number and eV is an electron volt, which is a unit of energy.

Explanation of statements:
a) The radius of the orbits is an integral multiple of Bohr's radius (0.053 mm).
This statement is true. According to the Bohr model, the electron in a Hydrogen atom revolves around the nucleus in circular orbits. These orbits have a fixed radius, which is given by the formula:

r = n^2 Bohr's radius

where n is the principal quantum number. Therefore, the radius of the orbits is an integral multiple of Bohr's radius.

b) The angular momentum is n times h/2π.
This statement is true. The angular momentum of an electron in a Hydrogen atom is given by the formula:

L = n h/2π

where n is the principal quantum number, h is Planck's constant, and π is the mathematical constant pi.

c) The energy in the nth orbit is n times the ground state energy.
This statement is false. The energy levels in a Hydrogen atom are given by the formula:

E = -13.6 eV/n^2

where n is the principal quantum number. Therefore, the energy in the nth orbit is proportional to 1/n^2, not n.

d) None of the above.
This statement is false. Statements a and b are true, while statement c is false.

Conclusion:
In conclusion, for a Hydrogen atom, statements a and b are true, while statement c is false. The Bohr model provides a simplified explanation of the structure of the Hydrogen atom, and its predictions have been verified experimentally.

(b)