CHEM 121: Lecture 13

Lyman Series

- A set of spectral lines that appear in the UV region when a hydrogen atom undergoes a transition from energy levels n>1 to n=1

Balmer Series

- A set of spectral lines that appear in the visible light region when a hydrogen atom undergoes a transition from energy levels n>2 to n=2

New Equation for Energy of Photon

- Change in E can be negative or positive but wavelength can not be negative

Why is Bohr's model inadequate?

- Does not fit the emission spectra of atoms and ions with more than one atom

Where is the electron in a hydrogen atom usually found?

- In the orbit closest to the nucleus (n=1) which is its ground state

What did Bohr's model predict?

- It predicted all of the hydrogen atom spectral lines

What conclusion can we draw from the de Broglie wavelengths of an electron versus a baseball?

- Large objects have short wavelengths - Short objects have large wavelengths

de Broglie Equation for Wavelength of Particle

- Linked it to momentum - Substituted momentum (p) to product of the mass of the particle (m) to its velocity (u) Ex. - λ = h/p = h/mu

Can we predict the location of an electron?

- No exactly

Born on Quantum Mechanics

- Statistical approach - The wave is not a real wave but a probability wave - Determining the exact position of the electron is impossible and squaring the wave function only gave the probability of the electron being in a certain region of space

How does the Bohr model explain the emission spectrum of hydrogen and other one-electron species?

- Taking into account the nuclear charge

Calculate the change in energy associated with the transition of the electron in the hydrogen atom from n = 2 to n = 1 and the corresponding wavelength of light (in nm) that would be released. What is the classification of this emitted electromagnetic radiation?

- This is for level 1 to level 2 and the corresponding wavelength of light that would be absorbed

The transition of the electron in the hydrogen atom from n = 6 to n = 2 corresponds to the shortest wavelength in the hydrogen emission (line) spectrum. Calculate this wavelength (in nm) and see if it agrees with the experimental data.

- This is from 4 to 2 and the wavelength is 486.3 nm

What did Schrodinger add?

- Three dimensional analogs/electron orbitals/standing waves

What is Schrodinger's view on wave functions?

- Wave function in wave mechanics were complex numbers and only by squaring the wave function could the electric charge density of the electron at location x at time t be determined

Wave Mechanics

- Wave nature of the electron

Standing Waves

- Waves are stationary and do not travel the length of the string - Applied to hydrogen atom - Only certain circular orbits have a circumference into which a whole number of wavelengths of the standing electron wave will "fit." All other orbits would produce destructive interference of the standing electron wave and are not allowed. - A whole number of half-wavelengths can be fitted into the circumference of the Bohr model orbit

Who is credited for the creation of quantum mechanics and who built on de Broglie's ideas?

- Werner Heisenberg - Erwin Schrodinger

Hydrogen Line Emission Spectrum

- When a high energy discharge is passed through a sample of hydrogen gas, the H_2 molecules absorb energy causing some of the H-H bonds to break - Instead of showing all the wavelengths of visible light, only certain energies that are allowed for the electron in the hydrogen are shown - Only certain wavelengths of emitted light are shown with changes in energy between discrete energy levels

Excited States

- When an electron in a hydrogen atom occupies higher energy levels

Paschen Series

- When electron cascades from level higher down to n=3

Schrodinger Equation

- Ψ (wave function) - Function of coordinates of electron's position in three-dimensional space - H is a set of mathematical instructions called an operator that acts on a function to produce another function