C. Quantum Theory and Electronic Structure of Atoms

Question 1

Hydrogenic atoms are ____ while many-electron atoms are ____

Answer 1

Hydrogenic atoms are atoms that are hydrogen-like which have only one electron and so are free of electron repulsions

H+, He+, and C5+

Many-electron atoms are atoms with more than one electron.

Question 2

Spectroscopic observations on hydrogen atoms suggest that an electron can occupy only _____

Answer 2

certain energy levels

Question 3

Emission of discrete frequencies of electromagnetic radiation occurs when an _____

Answer 3

electron makes a transition between certain energy levels

Question 4

All wavelengths (λ) can be described by this expression according to Johann Rydberg:

Answer 4

1/λ = R [(1/ni^2) - (1/nf^2)]

R - Rydberg constant = 1.097E7 m-1

Question 5

In Rydberg’s expression, quantum numbers (n) are mentioned which describes the ____

Answer 5

discrete energy levels that an electron can occupy

Question 6

Name the series and EMR region given the final quantum number:
nf = 1
nf = 2
nf = 3
nf = 4
nf = 5
nf = 6

Answer 6

nf = 1 → Lyman, UV
nf = 2 → Balmer, visible
nf = 3 → Paschen, IR
nf = 4 → Bracket, IR
nf = 5 → Pfund, IR
nf = 6 → Humphreys, Far IR

Land Bank of the Philippines, Beh Pafund Ha

Question 7

What is wave-particle duality?

Answer 7

Electrons can behave as particle or as waves the same as electromagnetic radiation can behave as particles (photons) or as waves (interference/diffraction)

Question 8

Define Heisenberg’s uncertainty principle

Answer 8

Given the wave-particle duality of electron and EMR, the linear momentum (m × a) and the location cannot be determined simultaneously

Question 9

How is quantization of energy shown through the Schrodinger equation?

Answer 9

solutions for Schrodinger equation only exists at certain value of E

Question 10

The probability of finding an electron at a given location is proportional to ____ at that point

Answer 10

the square of the wavefunction Ψ^2 = probability density

Question 11

Addition of positive region of a wavefunction to another positive region of another wavefunction will result to ____

Answer 11

constructive interference = enhanced probability of finding electron at that region

Question 12

Addition of positive region of a wavefunction to the negative region of another wavefunction will result to ____

Answer 12

destructive interference = reduces the probability that an electron will be found in that region

Question 13

Define five quantum number n, l, ml, s, and ms

Answer 13

1. principal quantum number (n) - energy, size of orbital, distance to nucleus
2. orbital angular momentum quantum number (l) - magnitude of orbital angular momentum (energy subshells) and angular shape
3. magnetic quantum number (ml) - orientation of that angular momentum, no. of orbitals in subshells
4. spin angular momentum (s) - analogue of l for orbital motion but it is restricted to the single, unchangeable value s=1/2
5. spin magnetic quantum number (ms) - refer to spin-up and spin-down; ms = +1/2 or -1/2

Question 14

Energy of the electron in a bound state is _____ than a widely separated stationary electron and nucleus as shown with the ___ values in allowed energy formula

Answer 14

lower
negative values of allowed energy

Question 15

The energy levels ____ as the energy increases

Answer 15

converge (becomes less negative)

Question 16

All orbitals with a given value of n belong to the same ______, all orbitals of a given n with the same value of l belong to the same ______, and individual orbitals are distinguished by the ____

Answer 16

n → shell
l → subshell (under same n)
value of ml

Question 17

Shells with n = 1, 2, 3, 4, …. is referred as ____ (notation)

Answer 17

n = 1 → K
n = 2 → L
n = 3 → M
n = 4 → N

Question 18

Subshell designation based on value of l and formula for l

Answer 18

l = n-1

l = 0 → s
l = 1 → p
l = 2 → d
l = 3 → f
l = 4 → g ….

Question 19

How many individual atomic orbitals does a d subshell of an atom have?

Answer 19

1. d → l = 2
2. ml = 2l + 1
3. ml = 5 → +2, +1, 0, -1, -2

Question 20

Which set of orbitals is defined by n = 4 and l =1? How many orbitals are there in this set?

Answer 20

l = 1 → p
ml = 2l + 1 = 2(1) + 1 = 3

three 4p orbitals → +1, 0, -1

Question 21

The number of nodes ___ as energy (n) increases

Answer 21

increases

Question 22

Regions where wavefunctions pass through zero are called ____

Answer 22

nodes

Question 23

The radial wavefunction of 1s orbital, [n=1, l=0, and ml=0] has ___ radial nodes and _____ as distance from nucleus increases

Answer 23

zero nodes (never passes through zero)
approaches zero (decays exponentially) as distance from nucleus increases

Question 24

As principal quantum number of an electron increases, it is found _____ the nucleus, its radial node ____, and its energy _____

Answer 24

further from nucleus → ↑nodes → ↑E

Question 25

The first occurrence of all orbitals other than s orbitals ____ at the nucleus

Answer 25

vanishes (zero) WHY? only s orbital has orbital angular momentum l=0 → electrons on the nucleus is from the 1s orbital only

Question 26

How to know the number of radial nodes of a given orbital?

Answer 26

radial nodes = n - l - 1

Question 27

A radial distribution function gives the ____

Answer 27

probability that an electron will be found at a given distance from the nucleus, regardless of the direction.

Question 28

The most probable distance from nucleus to find an electron ___ as the nuclear charge _____ because ____

Answer 28

decreases as the nuclear charge increases because electron is attached more strongly to the nucleus

Question 29

The most probable distance from nucleus to find an electron ___ as principal quantum number ____ because ___

Answer 29

The most probable distance increases as n increases because the higher the energy, the more likely it is that the electron will be found far from the nucleus.T

Question 30

The ___ of an orbital indicates the region of space within which the electron is most likely to be found

Answer 30

boundary surface

Question 31

How many nodal planes does p orbital has?

Answer 31

one for each orbital [p → l = 1] an orbital with the quantum number l has l nodal planes

Question 32

Difference in the orbital of H and He atom

Answer 32

He orbital will be more compact because it has greater nuclear charge (1s^2; 2 electrons) → electrons are closer to nucleus

Question 33

Effective nuclear charge accounts the effect of ____ and the reduction of actual nuclear charge to effective nuclear charge is called ____

Answer 33

repulsive forces from other electrons in a many-electron atom shielding Z eff = Z - σ σ - shielding constant

Question 34

The closer to the nucleus that an electron can approach, the ___ is the value of Z eff to Z because ____

Answer 34

closer because the electron is repelled less by the other electrons present in the atom

Question 35

Why 2s orbital is filled first before 2p despite having the same principal quantum number?

Answer 35

2s electron can experience penetration to the core (1s - filled inner shells of electrons) 2p orbital is more shielded by core electrons

Question 36

The order of subshell energies in many-electron atoms is ______ because ____

Answer 36

s < p < d < f because in a given shell, s orbitals are the most penetrating and f orbitals are the least penetrating.

Question 37

Discuss the electron configuration principles

Answer 37

1. Aufbau (building-up) - electrons fill atomic orbitals in order of increasing energy levels. 2. Pauli exclusion - two e- only per orbital, opposite spin if two (no two electrons in the same atom can have the same set of four quantum numbers) 3. Hund's rule - degenerate (same energy, same l) atomic orbitals are occupied singly before being paired 4. Madelung's Rule - Orbitals with lower n + l value are filled first (e.g., 4s [4+0] before 3d [3+2])

Question 38

Why atomic orbitals are occupied singly before being paired (must have parallel spin)?

Answer 38

Due to spin correlation, parallel spins of electron repel each other less. Half-filled shells with parallel spins are also more stable

Question 39

The increase in Zeff between C and N is 0.69 whereas the increase between N and O is only 0.62. Suggest a reason why the increase in Zeff for a 2p electron is smaller between N and O than between C and N given the configurations of the atoms listed above.

Answer 39

C: [He]2s^2 2p^2 N: [He]2s^2 2p^3 O: [He]2s^2 2p^4 C→N: occupies an empty p orbital N→O: occupies an already pilled p orbital (electron-electron repulsion is higher, lower Zeff, farther from nucleus)

Question 40

Why the electron configuration of Cr is [Ar]4s^1 3d^5 instead of [Ar]4s^2 3d^4?

Answer 40

spin correlation → less electron-electron repulsion → lower total energy → more stable

Question 41

Why the electron configuration of Cu is [Ar]4s^1 3d^10 instead of [Ar]4s^2 3d^9? Similarly, why [Kr]4d^10 instead of [Kr]5s^2 4d^8?

Answer 41

A filled d subshell will produce less electron-electron repulsion → lower total energy → more stable

Question 42

If the electron configuration of Ti (Z=22) is [Ar]4s^2 3d^2 what is the electron configuration of Ti3+?

Answer 42

[Ar]3d^1 for d-block (transition) elements forming cations, the s electrons are always lost before the d electrons

Question 43

Mnemonics for EMR

Answer 43

Rich Man In Vegas Use eXpensive Gadgets Radio Microwave Infrared Visible Ultraviolet X-ray Gamma Rays

Question 44

Arrange electromagnetic radiation in increasing order of wavelength

Answer 44

Gamma rays 1 pm to 10pm X-rays 10 pm to 10 nm Far UV Near UV 100 nm to 400 nm Visible 400 to 760 nm Near IR Far IR 760 nm to 1 mm Microwaves Radar 1mm to 1 m Radio waves 1 m to 1 km

Question 45

Proposed that light is emitted in discrete energy packets called ____

Answer 45

Max Planck quanta (quantum sing.)

Question 46

Proposed that light behaves as a stream of particles called _____

Answer 46

Albert Einstein photons

Question 47

Describe photoelectric effect

Answer 47

Light of certain frequencies causes electrons to be ejected from a metal surface to prove the particle nature of light.

Question 48

Explain atomic spectra

Answer 48

Electrons absorb or emit specific photon energies as they jump between energy levels, producing discrete spectral lines

Question 49

When atom from low energy level jump to high energy level, energy is _____

Answer 49

Energy is absorbed by the atom

Question 50

When atom from high energy level jump to low energy level, energy is _____

Answer 50

Energy is released (atom emits energy)

Question 51

When excited electrons fall to lower orbits (energy level), they ____

Answer 51

emit light (photon) at specific wavelengths with energy equal to difference between the two levels

Question 52

Who developed quantum mechanics to account for the wave-particle duality?

Answer 52

de Broglie (equation), Heisenberg, and Schrodinger

Question 53

Selection rules for the allowed energy level transitions

Answer 53

Δl = ± 1 Δ ml = 0, ±1

Question 54

Metal ion/s that will produce red flames

Answer 54

Li+ Ra2+ Sr2+

Question 55

Metal ion/s that will produce red-violet flames

Answer 55

Rb+

Question 56

Metal ion/s that will produce violet flames

Answer 56

K+ Cs+

Question 57

Metal ions that will produce yellow flames

Answer 57

Na+ Fe2+ Fe3+

Question 58

Metal ions that will produce orange flames

Answer 58

Ca2+

Question 59

Metal ions that will produce green flames

Answer 59

B3+ Ba2+ Sb3+ Sb5+

Question 60

Metal ions that will produce blue-green flames

Answer 60

Cu2+ Zn2+

Question 61

Metal ions that will produce blue flames

Answer 61

In3+ Se2+ Se4+ Pb2+ As3+

Question 62

Electrons with the highest principal quantum number are called ____ and those in lower energy levels are ___

Answer 62

valence electrons inner electrons

Question 63

Species with the same electronic configuration

Answer 63

isoelectronic species

Question 64

How many orbitals (ml) in a 2s orbital?

Answer 64

Subshells = 2l+1 = 2(0)+1 = 1

Question 65

How many electrons in a 2s orbital?

Answer 65

Subshell = 2(2l+1) = 2(2(0)+1) = 2

Question 66

How many orbitals and electrons in a n=2 shell?

Answer 66

orbitals = n^2 = 2^2 = 4 electrons = 2n^2 = 2(2^2) = 8

Question 67

How many subshells and orbitals in a n=4 shell?

Answer 67

4 subshells l = 0(s), 1(p), 2(d), 3(f) 4s, 4p, 4d, 4f orbitals = n^4 = 4^4 = 16 = 1(s)+3(p)+5(d)+7(f) = 16 | shell number = subshells in a shell | orbitals: s=1; p=3; d=5; f=7; g=9