Chapter 6

Calculate the energy of the emitted photon when an electron moves from n=6 to n=2 in a hydrogen atom. What is the wavelength of the radiation? Is this line in the visible region? If so, what color?

411 nm magenta

The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. what is the frequency of this radiation?

5.09 x10^14 s^-1

The Photoelectric Effect and Photons (Albert Einstein)

When photons of sufficient energy strike the surface of a metal, energy is transferred to the electrons and they are emitted. Radiant (light) energy itself is quantized. Ephoton=hv Ephoton=energy of a single photon h=6.626x10^-34 J/s v=frequency

Magnetic quantum number (ml)

can have integral values between -l and +l, including zero. The quantum number describes the orientation of the orbital in space

Angular momentum quantum number (l)

can have integral values from 0 to (n-1) for each value of n. This quantum number defines the shape of the orbital.

Principal quantum number (n)

can have positive integral values 1, 2, 3...∞. As n increases, the size of the orbital becomes larger and the electron is farther away from the nucleus

Electromagnetic radiation (radiant energy)

characterized by its wave nature. Examples: visible light, radio frequency, and infrared rays

A continuous spectrum

contains light of all wavelengths

Radial probability function

defined as the probability that we will find an electron at a specific distance from the nucleus

Spin magnetic quantum number (ms)

describes the spin of an electron. The spin is either +1/2 or -1/2

Relationship between frequency and energy

direct

Aufbau principle

orbitals are filled in order of increasing energy

wavelength

the distance between two adjacent peaks

Core electrons

the inter electrons and do not participate in bonding. they are located in the lower energy levels

line Spectra

the light emission only at specific wavelengths

frequency

the number of complete wavelengths that pass a given point at each second (in inverse seconds) -most commonly reported in hertz (Hz)

Valence electrons

the outermost electrons in an atom that participate in bonding. They are located in the highest energy level(s)

A laser emits light that has a frequency of 4.69x10^14 s^-1. What is the energy of one photon of this radiation?

3.11x10^-19 J

An FM radio broadcasts at 89.3 MHz. calculate the wavelength.

3.36 m

calculate the energy of one photon of yellow light that has a wavelength of 598 nm. (Frequency given is 5.09x10^-14 s^-1)

3.37x10^-19 J

the spin magnetic quantum number

(ms) describes the spin of an electron and can be +1/2 and -1/2

Line Spectra and the Bohr Model

-Bohr calculated the energies (E) corresponding to allowed orbits -each allowed orbit corresponds to a different value of n (whole number) -the radius of the orbit gets larger as n increases

Absorption of energy

-electron absorbs a photon of energy; transitions from lower to higher energy level - difference in energy= +ΔE -+Ephoton=+ΔE -+Energy gap=+ΔE

Emission of energy

-electron releases a photon of energy; transitions from higher to lower energy level -difference in energy= -ΔE +Ephoton= -ΔE -+Energy gap= -(-ΔE)

Energy gap (ΔE)

-equal to Ephoton -is always positive

For l=2d, what are the possible values of ml?

-l=0...(n-1) ml= 2, 1, 0, -1, -2

Give the numerical values of n and l corresponding to each of the following orbital designations.

3p: n=3, l=1 2s: n=2, l=0 4f: n=4, l=3 5d: n=5, l=2

Bohr's model

1. Only orbits of certain radii, corresponding to certain specific energies, are permitted for the electron in a hydrogen atom. 2. An electron in a permitted orbital is in an "allowed"energy state. It does not radiate energy or spiral into the nucleus. 3. Energy is emitted or absorbed by the electron only as the electron chawed from one allowed energy state to another. This energy is emitted or absorbed as a photon that has energy (E=hv).

Indicate whether energy is emitted or absorbed in hydrogen: 1. From n=2 to n=6 state 2. From an orbit of 4.76A to one of radius 0.529 A (1A= 1x10^-10m) 3. From n=6 to the n=9 state

1. absorption 2. emission 3. absorption

The Rydberg equation

1/wavelength = RH (1/n1^2 - 1/n2^2) RH= 1.0968x10^7 m^-1

the speed of light

3.00 x 10^8 m/s

What is the wavelength of an emitted photon for transition from n=3 to n=2? What color is the observed light (photon)?

565 nm Red

Planck's constant

6.626x10^-34 J/s

Electron configuration principles

Aufbau Principle Pauli exclusion principle

Quantization of Energy (Max Planck)

Electromagnetic energy can be either released or absorbed by atoms only in "fixed amounts" of some minimum size. E=hv E= energy of a single quantum h=6.626x10^-34 joule-second (J-s) v=frequency of the light (radiation)

Value of l and letter used

Value of l: 0, letter used: s Value of l: 1, letter used: p Value of l: 2, letter used: d value of l: 3, letter used: f

For s- and p-block elements:

electrons located in filled d- or f-shells are not considered to be valence electrons

For d-block elements:

electrons located in filled f-shells are not considered to be valence electrons

Relationship between frequency and wavelength

inverse

Relationship between wavelength and energy

inverse

For n=4, what are the possible values of l?

l-0...(n-1) l= 0 (s), 1 (p), 2 (d), 3 (f)

If ml=2, what are the possible values of l?

l=2, 3 ml=2

Bohr Model

model of the atom in which electrons move rapidly around the nucleus in paths called orbits

Pauli exclusion principle

no more that 2 electrons per orbital

spectrum

produced when radiation is divided into its component wavelengths (i.e. a rainbow)

Polychromatic

radiation composed of many different wavelengths

Monochromatic

radiation composed oof a single wavelength

The Pauli exclusion principle

states that no 2 electrons in an atom can have the same set of four quantum numbers (n, l, ml, and ms)

Louis de Broglie

suggested that an electron moving about the nucleus of an atom behaves like a wave and therefore has a wavelength.

The wavelength of the electron (or any particle) depends on its mass (m) and velocity (v)

wavelength e= h/mv

If an electron transitions (moves) from an initial state (ni) to a final state (nf), then the change in energy (ΔE) can be calculated using the following equation

ΔE=(-2.18x10^-18 J)(1/nf^2-1/ni^2) -if ΔE is negative, energy (or a photon) was emitted -if ΔE is positive, energy was absorbed