Question

(Bohr model of the atom.) Consider an electron in a circular orbit around a proton. Assume the angular momentum can only take on values equal to nℏ where n is an integer (n=1,2,3,…) and ℏ is a constant. Determine the possible values of the radius for the orbit and the possible values for the total energy. Make up a table of the energy for the first four energy states (that is, for the electron in the four smallest orbits).

Answer 1

In the Bohr model, the radius of the electron's orbit and the total energy are determined by quantized angular momentum. The first four energy states can be represented in a table.

Step-by-step explanation:

In the Bohr model of the atom, the angular momentum of an electron in its orbit is quantized, meaning it can only take on specific, discrete values. The angular momentum, denoted by L, is given by the formula L = nℏ, where n is an integer and ℏ is Planck's constant. The radius of the orbit, denoted by rn, can be calculated using the formula rn = αn^2, where α is a constant.

The total energy of the electron in each orbit is determined by the equation E = -13.6/n^2 eV, where n is the principal quantum number. The first four energy states can be represented in a table as follows:

n Radius (rn) Total Energy (E)

1 0.529 Å -13.6 eV

2 2.12 Å -3.4 eV

3 4.76 Å -1.51 eV

4 8.47 Å -0.85 eV