Using the Bohr model of hydrogen, find the linear momentum, when n=3.

To find the linear momentum using the Bohr model of hydrogen when n=3, we need to first understand the formula for linear momentum in the context of quantum mechanics.

In quantum mechanics, an electron is described as a wave function, which includes both position and momentum information. The momentum of an electron in the Bohr model is related to the principal quantum number (n) through the formula:

p = n * h / (2πr),

where:
- p represents the linear momentum of the electron,
- n is the principal quantum number (in this case, n=3),
- h is the Planck's constant (approximately 6.626 x 10^(-34) J.s),
- r is the radius of the electron's orbit.

In the Bohr model, the radius of the electron's orbit is given by the formula:

r = a₀ * n² / Z,

where:
- a₀ is the Bohr radius (approximately 0.529 x 10^(-10) m),
- Z is the atomic number of the nucleus (for hydrogen, Z=1).

Substituting the value of r into the momentum formula, we get:

p = n * h / (2π * (a₀ * n² / Z))

p = (n * h * Z) / (2π * a₀ * n²)

Now, let's substitute the given values into the formula:

p = (3 * (6.626 x 10^(-34) J.s) * 1) / (2π * (0.529 x 10^(-10) m) * 3²)

p = (3 * 6.626 x 10^(-34) J.s) / (2π * 0.529 x 10^(-10) m * 9)

After calculating the expression, we obtain the value of the linear momentum for n=3 in the Bohr model of hydrogen.