CHM2041 Chapter 8 Atomic Structure

Calculating Energy Difference, (Triangle)E, between 2 levels

(triangle)E= I E(final) - E(initial) I = R(H)(1/n(f)^2 - 1/n(i)^2) -R(H)= 2.18x10^-18

1. Principle Quantum Number, n

- n = 1, 2, 3, 4.....infinity (indicates shells) -as n increases, so does size, energy and electron capacity -the electrons energy depends principally on n - E = -RHc/n(i)^2 = -2.179 x 10^-18 J/ n(i)^2

Planck's Equation

-an object can gain or lose energy by absorbing or emitting radiant energy in quanta of specific frequency (v) -E=hv=h(c/lambda) -E= energy of a photon -h= planck's constant= 6.626x10^-34 Jxs/photon

Bohr model of atom

-energies of e are quantized: e occupy certain orbits of specific energies -bohr's theory correctly explains the H emission spectrum and those of hydrogen-like ions (He+, Li2+, Be3+....etc.; 1e species) -the theory fails for all other elements (treats electron as particle) -the wave nature of the electron: deBroglie

The Photoelectric Effect

-light can strike the surface of some metals causing electrons to be ejected (light: specific v or E) -demonstrates the particle nature of light

Orbital

-region of space within which one can expect to find an electron (wave function of e in an atom) -no solid boundaries (cloud) -electron capacity: 2e per atomic orbital -space surrounding nucleus divided up into large volumes called shells -shells subdivided into smaller volumes called sub shells -orbitals located in sub shells -shells, sub shells, and orbitals described by 3 or 4 quantum numbers

3. Magnetic Quantum number, ml

-specifies spacial orientation ml = -l, (-l+1), (-l+2), ......0,......, (l-2), (l-1), +1

Wave Nature of Electron

-wavelike properties of matter -lambda= h/mv = h/p -h: planck's constant -m: mass of moving particle -v: velocity of particle p=mv: momentum

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

0, 1, 2, 3

The de Broglie equation relates the wavelength and the kinetic energy of particles. What is the wavelength, in nanometers, associated with an electron with a speed of 3.42 × 106 m/s?

0.213

Consider the shape of a typical p orbital. How many nodal planes are visible for the 2p orbital?

1

How many s orbitals exist in one energy level of an atom?

1

Basic Postulates of Quantum Theory

1. Atoms and molecules exist in certain energy states. Atoms and molecules change energy states by absorbing or emitting enough energy to bring it to a new energy state (the quantum condition) 2. atoms or molecules absorb or emit radiation (light) to change their energies. The V and lambda of light emitted or absorbed are related to the energy change by: E= hv = hc/lambda 3. allowed energy states of atoms and molecules can be described by quantum numbers - quantum numbers: solutions of the schrodinger, Heisenberg, and Dirac equations

A metal must absorb radiation with a frequency of 2.18x1015 s-1 in order to eject an electron from its surface. Which wavelength of radiation does this correspond to?

138nm

How many total orbitals are there with principal quantum number of n= 4?

16

Which of the following orbital represents impossible combinations of nand l quantum numbers?

1p

1 angstrom =

1x10^-10 m = 1x10^-18 cm

How many nodes does the 3s orbital possess?

2

How many orbitals can have quantum numbers of n = 3 and ml = −1?

2

The number of orbitals in any sublevel is equal to

2l+1

Which electron is, on average, closest to the nucleus?

2s

Which choice ranks the given orbitals in order of increasing size?

2s < 3s < 4s

Calculate the energy of 1 mole of photons which has a wavelength of 322 nm.

372 kJ

ROY G BIV Radiation

380-750 nm; eyes detect this radiation

What is the energy of a photon with a wavelength of 492 nm?

4.04 x 10^-19 J

What is the wavelength of the radiation associated with an electron moving from energy level n = 6 to energy level n = 2 in a Bohr hydrogen atom?

410nm

Which orbital is indicated by the quantum numbers n = 4, l = 2, ml = +2?

4d

Which orbital is indicated by the quantum numbers: n = 4, l = 2, ml = −0?

4d

Which electron transition produces light of the highest frequency?

6p to 1s

Select the correct statements.

A node is a point where the wave function (𝜓) passes through zero The probability of finding the electron at a node is zero.

Schrodinger's equation

H (wavelength: looks like a trident) = E (wavelength)

What is the general form of the Schrödinger equation?

H𝜓 = E𝜓

Select the incorrect statement.

In the case of a macroscopic object, its wavelength is observable.

Which of the following resembles most closely, the uncertainty principle?

It is impossible to know at the same time, the exact position and momentum of an electron

What is the radial distribution function?

It represents the total probability of finding the electron in a small spherical shell at a distance r from the nucleus.

Select the statement or information which is not correct.

The 3p, 4p, 5p, and higher p orbitals all have different shapes.

What is the photoelectric effect?

The ejection of electrons from a metal surface when it is struck with light of sufficient energy.

Which of the following statements is correct?

When the hydrogen atom absorbs energy in the form of electricity, it can reemit that energy as light.

Planck suggested that all energy gained or lost by an atom must be some integral multiple of a minimum amount of energy called ________

a quantum

Energy is absorbed....

an e in an atom jumps from ground level (n=1) to upper levels (n>1) -atom is now in an excited state (absorption spectrum)

Which electron is, on average, closest to the nucleus?

an electron in a 2s orbital

Atomic line spectra and the Bohr atom

an emission spectrum is formed when an electric current passes through a gas in a vacuum tube (very low pressure) causing the gas to emit light -sometimes called a bright light spectrum

Rydberg Equation

an empirical equation that predicts the wavelengths of the lines in the hydrogen spectrum - 1/lambda= R(1/n(1)^2 - 1/n(2)^2) -R= 1.097 x10^7 m^-1 -the n's refer to the numbers of the energy levels in the emission spectrum of hydrogen

Four Quantum Numbers

describe energy states and orbitals of electrons in atoms (n, l, m, ms)

speed of propagation, c

distance traveled by ray per unit time in vacuum; all electromagnetic radiation travel at same rate (speed of light) = 2.998x10^8

wavelength (lambda)

distance traveled by wave in 1 complete oscillation; distance from the top (crest) of one wave to the top of the next wave; or successive troughs or nodes

Energy is emitted....

e jumps down from upper levels to lower levels; absorbed energy is then emitted as light; emission of photons (emission spectrum)

Electromagnet Radiation

energy can be transformed between atoms and molecules in the form of light or electromagnetic

Select the appropriate combination that will complete the following: The________ of a photon of light is ________ proportional to its frequency and ________ related to its wavelength.

energy, directly, inversely

The number of complete waves that pass through a point in a given period of time is known as the ..........

frequency

The probability density function, 𝜓2

is the probability per unit volume, of finding the electron at a point in space

Uncertainty Principle

it is impossible to determine both the position (x) and the momentum (p) of an electron simultaneously - e does not orbit the nucleus in defined paths (no orbits)

2. Angular Momentum Quantum, l

l = 0, 1, 2, 3, 4.....(n-1) always n > l l = s, p, d, f, g...... (sub shells) - l indicates the shape of the orbital - orbitals are the volume around the nucleus that the electrons occupy 90-95% of the time

What are all the values of l when n = 3?

l=0, 1, 2

Which electron in a hydrogen atom is normally the closest to the nucleus?

n = 1, l = 0, ml = 0, ms = +1/2

Which of the following transitions in the Bohr hydrogen atom, results in the absorption of the greatest amount of energy.

n = 2 to n = 5

Which of the following transitions in the Bohr hydrogen atom, results in the absorption of the greatest amount of energy.

n = 2 to n = 8

Give the values of the quantum numbers n and l for the 3p orbital.

n = 3; l = 1

In a given atom, which of these transitions would result in the emission of a photon with the shortest wavelength?

n = 4 to n = 1

Give the values of the quantum numbers n and l for the 4p orbital.

n = 4; l = 1

Which of the following orbitals represents impossible combinations of the n and l quantum numbers?

n = 4; l = 4

Each orbital is specified by three quantum numbers. Select them.

n, l, ml

S orbital

n=1 l=0 ml=0 shape: sphere one type of s orbital

p orbitals

n=2 l=1 ml=-1, 0, 1 one node in shape 3 types of p orbitals

d orbitals

n=3 l=2 ml=-2, -1, 0, 1, 2 5 types of d orbitals

f orbitals

n=4 l=3 ml=-3, -2, -1, 0, 1, 2, 3 7 types of f orbitals

transverse wave

perpendicular oscillating electric and magnetic fields

trident^2

probability of finding the e at a point in space

The wavelength and frequency of a wave are directly related to which other wavelike property?

speed

The lowest energy orbital is the

the 1s orbital

What does the angular momentum quantum number signifies?

the shape of the orbital

all visible and invisible wavelengths are called

ultraviolet radiation

It is not possible to know exactly, the electron's position and momentum at the same time. This is known as the

uncertainty principle

dual nature of light

wave and particle

Waves may be described by their

wavelength, frequency, amplitude, speed