University:
North Idaho College
Course:
PHYS-211 | Engineering Physics I
Academic year:

2023
Views:

103

Pages:

4
Author:

Hani T.

*BOHr MODEL 8 The Rutherford model of the atom assumed that the electrons move around the Nucleus. The Bohr Model is a significant improvement over this as it quantifies the motion of electrons around the Nucleus By Postulating Circular orbits. The Basic feature in the Model is that the Coulombic attraction Between the Nucleus and electrons equals the centripetal force needed to Keep the electrons in the Circular orbit That is: F_Coulomb = K * e^2 / r^2 F_centrifugal = m_e * acceleration = m_e * v^2 / r m_e * v^2 / r = K * e^2 / r^2 Furthermore, the angular MOMENTum (m_e * v * r) is quantized and equals n * h / 2 * pi r = h^2 * n^2 / 4 * pi^2 * m_e * K The Bohr Model puts restrictions on the allowed orbits for hydrogen. The radius of the orbit is proportional to n². Substituting the fundamental constants, we obtain r = n² x (52.9 x 10^-12) m n = 1 refers to the first orbit whose radius is 52.9 pm (0.529 Å) and this value is known as the Bohr radius. This value is the unit of length in atomic units. In order to obtain the energies, the sum of the kinetic and potential energies can be written as: E = E_kin + E_pot = (1/2 * m_e * v^2) - (K * e^2 / r) Since: m_e * v^2 / 2 = K * e^2 / 2r E = - K * e^2 / r E = - [ (4 * pi^2 * K * m_e * c^2) / h^2 ] * (1 / n^2) E = - R_H * Z^2 / n^2 Since R_H = (4 * pi^2 * K * m_e * c^2) / h^2 = 52.9 x 10^-12 E_n = - R_H * Z^2 / n^2