Atomic Structure and Periodicity

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A Change between Two Discrete Energy Levels

Slide 17

The Bohr Model

The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits. The energy levels available to the hydrogen atom:

E = energy of the levels in the H-atom

z = nuclear charge (for H, z = 1)

n = an integer, the large the value, the larger is the orbital radius.

Bohr was able to calculate hydrogen atom energy levels that exactly matched the experimental value. The negative sign in the above equation means that the energy of the electron bound to the nucleus is lower than it would be if the electron were at an infinite distance.

Slide 18

Electronic Transitions in the Bohr Model for the Hydrogen Atom

Slide 19

Ground State: The lowest possible energy state for an atom (n = 1).

Energy Changes in the Hydrogen Atom

E = Efinal state  Einitial state

= -2.178 x 10-18J

The wavelength of absorbed or emitted photon can be calculated from the equation,

Slide 20

Example: Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

Using Equation, with Z = 1 we have

E1 = -2.178 x 10-18 J(12/12) = -2.178 x 10-18 J

E2 = -2.178 x 10-18 J(12/22) = -5.445 x 10-19 J

E = E2 - E1 = (-5.445 x 10-19 J) – (-2.178 x 10-18 J)

= 1.633 x 10-18 J

Slide 21

The positive value for E indicates that the system has gained energy. The wavelength of light that must be absorbed to produce this change is

(6.626 x 10-34 J.s)(2.9979 x 108 m/s)

1.633 x 10-18 J

= 1.216 x 10-7 m

Slide 22

Example: Calculate the energy required to remove the electron from a hydrogen atom in its ground state.

Removing the electron from a hydrogen atom in its ground state corresponds to taking the electron from ninitial = 1 to nfinal = . Thus,

E = -2.178 x 10-18 J

= -2.178 x 10-18 J

The energy required to remove the electron from a hydrogen atom in its ground state is 2.178 x 10-18 J.

Slide 23

Quantum Mechanics

Based on the wave properties of the atom Schrodinger’s equation is (too complicated to be detailed here),

 = wave function