## To find the linear momentum of the hydrogen atom in its 11th excited state, n = 12, using the Bohr model, follow these steps:

Step 1: Determine the first Bohr orbit radius, 'a':

The first Bohr orbit radius, 'a', can be calculated using the formula:

a = 0.529 * Ã… (Bohr radius)

Step 2: Calculate the radius of the orbit, 'R', in the 11th excited state:

The radius of the 11th excited state orbit, 'R', can be determined using the formula:

R = n^2 * a

Substitute the value of 'n' as 12:

R = (12^2) * a

Step 3: Solve for the electron velocity, 'v':

To find the electron velocity, we can equate the centripetal force to the Coulomb force, which gives us the formula:

mv^2 / R = k * (e^2 / R^2)

Here, 'm' is the mass of the electron, 'v' is the electron velocity, 'k' is the Coulomb constant, and 'e' is the elementary charge.

Step 4: Rearrange the equation to solve for 'v':

Multiply both sides of the equation by 'R' and rearrange the terms to solve for 'v':

mv = k * (e^2 / R)

v = (k * e^2) / (m * R)

Step 5: Calculate the electron velocity, 'v':

Substitute the known values into the equation:

v = (k * e^2) / (m * R)

v = [(9 * 10^9 N*m^2/C^2) * (1.6 * 10^-19 C)^2] / [(9.1 * 10^-31 kg) * R]

Step 6: Calculate the linear momentum, 'p':

To find the linear momentum, 'p', multiply the electron mass, 'm', by the electron velocity, 'v':

p = m * v

Substitute the known values into the equation:

p = (9.1 * 10^-31 kg) * v

After performing the calculations, you will find the linear momentum of the hydrogen atom in its 11th excited state using the Bohr model.