The de Broglie wavelength associated with electrons revolving around the nucleus in a hydrogen atom in the ground state can be calculated using the de Broglie wavelength equation:

λ = h / p

Where:
λ is the de Broglie wavelength
h is the Planck's constant (6.626 × 10^-34 Js)
p is the momentum of the electron

To determine the momentum of the electron, we need to use the Bohr model of the hydrogen atom. According to the Bohr model, the momentum of the electron is given by:

p = mv

Where:
m is the mass of the electron (9.11 × 10^-31 kg)
v is the velocity of the electron

To find the velocity of the electron, we can use the equation for the centripetal force in circular motion:

Fc = mv^2 / r

Where:
Fc is the centripetal force
m is the mass of the electron
v is the velocity of the electron
r is the radius of the electron's orbit

In the ground state of the hydrogen atom, the electron revolves around the nucleus in the first energy level, which corresponds to the Bohr radius (a0) of approximately 0.529 × 10^-10 m.

The centripetal force in this case is provided by the electrostatic attraction between the electron and the nucleus, given by Coulomb's law:

Fc = ke^2 / r^2

Where:
ke is the electrostatic constant (8.988 × 10^9 Nm^2/C^2)
e is the elementary charge (1.602 × 10^-19 C)

By equating these two expressions for the centripetal force, we can solve for the velocity of the electron:

mv^2 / r = ke^2 / r^2

v^2 = ke^2 / mr

v = √(ke^2 / mr)

Now we can substitute the values into the equation for the de Broglie wavelength:

λ = h / (mv)

Substituting the values for h, m, and v, we can calculate the de Broglie wavelength associated with an electron in the ground state of a hydrogen atom.

The correct answer for the de Broglie wavelength is (3) 6.62.