Question

Consider a single electron Bohr atom in the n=12 state. a) find the orbital electron’s angular momentum. b) find the total energy of the atom

Answer 1

Answer 2

In a single electron Bohr atom, the angular momentum of the electron in the nth state can be calculated using the formula:

a) Angular momentum (L) = n * h / (2π)

Where: n = Principal quantum number (given as n=12 in this case) h = Planck's constant (approximately 6.626 x 10^-34 Js)

Let's calculate the angular momentum:

L = 12 * 6.626 x 10^-34 Js / (2π) L ≈ 2.514 x 10^-33 Js

b) To find the total energy of the atom in the nth state, we can use the formula for the energy of an electron in the Bohr model:

Total energy = (-(2.18 x 10^-18 J) / n^2)

Where: n = Principal quantum number (given as n=12 in this case) (-2.18 x 10^-18 J) is the negative of the ionization energy of hydrogen (also known as the Rydberg constant)

Let's calculate the total energy:

Total energy = (-(2.18 x 10^-18 J) / 12^2) Total energy ≈ -1.513 x 10^-19 J

Please note that the energy value is negative, indicating that the electron is in a bound state in the atom's nth energy level (n=12). The negative energy represents the binding energy of the electron in the atom.