CHEM 121: Lecture 14

How are the p orbitals labeled?

- According to which axis the lobes lie along

Degenerate

- All orbitals with the same value of n (principal quantum number) have the same energy

Magnetic Quantum Number (m_l)

- Can have integral values between -l and +l - Relates to the orientation in space of the angular momentum associated with the orbital

Angular Momentum Quantum Number (l)

- Can have integral values from o to n-1 for each value of n - Determines the value of the orbital angular momentum of the electron occupying the orbital and thus determines the shape of the atomic orbital

Where is hydrogen's single electron usually and why?

- Can occupy any of its atomic orbitals - Electron usually resides in the 1s orbital which is the lowest energy state

How do you find the energy of a particular orbital?

- Determine value of n

Principal Quantum Number (n)

- Determines the energy of the electron occupying the orbital and the size of the orbital - Can have integral values related to the size and energy of the orbital - Can only be positive

How are values of l addressed?

- Each is assigned a letter - l = 0 is s - l = 1 is p - l = 2 is d - l = 3 is f

Subshell

- Each value of l (momentum quantum number)

d Orbital Shape

- Have four lobes centered in a plane indicated in the orbital label - 5th shape has two lobes on z axis and a belt centered in the xy plane

p Orbital Shape

- Have two lobes separated by an angular node at the nucleus

What is the uncertainty principle?

- Imprecision in knowledge of simultaneous measurements of position and momentum

How do each orbital for the hydrogen atom have different probabilities?

- Probabilities differ based on orbital - There are areas of zero electron probability/nodes for 2s and 3s orbital - c is the surfaces that contain 90% of the total electron probability (orbital size)

Why can't the size of an orbital be precisely defined?

- Probability never becomes zero and the hydrogen 1s orbital has no distinct size

What did Heisenberg find?

- That we can not know both the position and the momentum of a particle at a given time - Where Δx is the uncertainty in position and Δp is the uncertainty in momentum

What is the normally accepted arbitrary definition of the size of the hydrogen 1s orbital?

- The radius of the sphere that encloses 90% of the total electron probability - 90% of the time the electron is found inside this sphere which yields a radius of 2.6 a_0 or 1.4 x 10^-10m (140pm)

What happens when n increases in the principal quantum number?

- When n is increasing there is higher energy because the electron is less tightly bound to the nucleus and the energy is less negative

Radial Probability Distribution

- Yields the probability of finding the electron in a certain orbital - The probability decreases over distance