Lesson 1: Quantum Numbers

Who proposed the atomic model in 1912- 1913 using the quantized orbits?

Neils Bohr

In Bohr’s atomic model, what does n represents?

energy level of an electron

What experimental data did Bohr’s model successfully explain?

emission sprectrum of hydrogen

Why did Bohr’s model raise questions about electron orbits?

electrons is only placed in a fixed distance

Why was Bohr’s model limited in its application?

it only woked for hydrogen and one-electron ions

Max Planck

Studied the radiation of hot objects. Continuous vs discreet energy. Analogy: Analog vs. Digital Clock. If packets of energy are discreet, there must be medium size for one of these packets. That packet is called the “quantum”.

In the early 1900s, a German physicist named Max Planck stated his quantum hypothesis, where he explained that radiation from a sparkling body changed its shades from red to orange to blue when the temperature was increased.

This phenomenon was also known as black body radiation.

Who proposed the quantum hypothesis in the early 1900s

Max Planck

What phenomenon did Max Planck study when observing radiation color changes with temparature?

Black Body Radiation

What did Planck discover about the nature of energy?

energy existed in singular units, just like matter, instead of consistent electromagnetic waves. With this assumption, it was made clear that energy was quantifiable

Why was Planck’s assumption about energy significant?

it showed that energy is quantifiable

What was the primary supposition of the quantum hypothesis?

that energy exists in quantized units

Later, Planck composed a numerical condition,

including a figure to express the individual units of energy. He termed it “quanta”. With this, he was further able to solidify his assumption about the findings. Planck won the the Nobel Prize in Physics for his hypothesis in 1918

Who explained the photoelectric effect using the quantum theory?

Albert Einstein

In 1905

Albert Einstein took the theory further by stating that radiation, apart from energy, is quantised in a similar way. He also used the hypothesis to explain the photoelectric effect.

What is photoelectric effect?

emission of electrons when light strikes at the surface

What property of light did Einstein emphasize in explaining the photoelectric effect?

LIght has particle like photons

Why was the photoelectric effect important to quantum theory

it showed that light has a quantisized energy

Special behavior of matter in the microscopic world was paid attention by Louis de Broglie

He asked the question: If electromagnetic radiation can have particle-like character, can electrons and other submicroscopic particles exhibit wavelike character? In his 1925 doctoral dissertation, de Broglie extended the wave- particle duality of light that Einstein used to resolve the photoelectric-effect paradox to material particles. He predicted that a particle with mass m and velocity v (that is, with linear momentum p) should also exhibit the behavior of a wave with a wavelength value A, given by this expression in which h is the familiar Planck's constant:

Louis de Broglie

a French physicist in the year 1924, also suggested that there is no major contrast in the behaviour of matter and energy. At the subatomic level, both can act either as waves or particles. This hypothesis is known as the principle of wave-particle duality. The same kind of duality must apply to the matter

What is the de Broglie wavelength a characteristic of?

Particles and bodies

How did de Broglie explain Bohr’s quantized orbits

electrons are circular standing waves

Who experimentally CONFIRMED the wave nature of electrons?

Davisson and Gerner

What did Schrodinger contribute to quantum theory in 1926?

wave equation for particles

What does Schrodinger’s equation describe about electrons?

Probability distribution of electrons

What did Heisenberg’s uncertainty principle state?

you cannot know both position and momentum exactly

Quantum Numbers

are important because they can be used to determine the electron configuration of an atom and the probable location of the atom’s electron. is described by a wave function that complies with the Schrödinger equation.

Each electron in an atom has a unique set of quantum numbers; according to the Pauli Exclusion Principle,

no two electrons can share the same combination of four quantum numbers.

Quantum numbers are also used to understand other characteristics

of atoms such as?

as ionization energy and the atomic radius.

Types of Quantum Numbers

principal quantum number, azimuthal quantum number, magnetic quantum number, spin quantum number

Principal Quantum Number

symbol (n): describes the energy of an electron and the most probable distance of an eletron from the nucleus. Size and energy of an orbit/shell: n; 1, 2, 3, 4, Greater value of n represents bigger orbital with high energies

What is the Principal Quantum Number (n) represents?

principal energy level

If n=3, what does it indicate?

third principal shell

What happens to an atomic size as (n) increases?

the atomic size increases

When the value of n is higher, the number of principal electronic shells is greater.

This causes a greater distance between the farthest electron and the nucleus. As a result, the size of the atom and its atomic radius increases.

Because the atomic radius increases, the electrons are farther from the nucleus. Thus it is easier for the atom to expel an electron because the nucleus does not have as strong a pull on it, and

the ionization energy decreases.

Why does ionization energy decrease as n increases?

electrons are farther, nucleus pulls less

How does atomic radius and ionization energy related when n increases?

Larger radius, lower ionization energy

Azimuthal Quantum Number

symbol: (l). It describes the shape of the orbital also known as Orbital Angular Momentum, Momentum Quantum Number, The value of (l) depends on the principal quantum number.

What subshells correspond to (l) values?

s,p,d,f

What is the azimuthal quantum number when the sublevel is s?

0 (zero)

What is the azimuthal quantum number when the sublevel is p?

1 (one)

What is the azimuthal quantum number when the sublevel is d?

2 (two)

What is the azimuthal quantum number when the sublevel is f?

3 (three)

What is the full name of the sublevel represented by s?

Sharp

What is the full name of the sublevel represented by p?

Principal

What is the full name of the sublevel represented by d?

Diffused

What is the full name of the sublevel represented by f?

Fundamental

What is the maximum number of electrons that can occupy an s sublevel?

2

What is the maximum number of electrons that can occupy a p sublevel?

6

What is the maximum number of electrons that can occupy a d sublevel?

10

What is the maximum number of electrons that can occupy an f sublevel?

14

Magnetic Quantum Number

symbol (m_l.) describes the energy level in a subshell. Explains the effect of an orbital in the magnetic field i.e the orientation of an orbital. Orbital split up into degenerate orbitals ( having same energy and size ) in a magnetic field. Each degenerate orbital can hold up to 2 electrons

What range of values (ml) can take?

-l to +l, including 0

s subshell (l = 0):

ml = 0 → 1 orbital

p subshell (l = 1):

ml = –1, 0, +1 → 3 orbitals

d subshell (l = 2):

ml = –2, –1, 0, +1, +2 → 5 orbitals

f subshell (l = 3):

ml = –3, –2, –1, 0, +1, +2, +3 → 7 orbitals

What does the (ms) spin quantum number represent?

direction of electron spin

How many electron can occupy 1 orbital?

2

What are the values of (ms)

-1/2, +1/2

How is spin up electron represented?

+1/2 upward arrow

Why do electrons in the same orbital need opposite spins?

to follow pauli exclusion principle

The Pauli exclusion principle declares that?

there can only be a maximum of two electrons for every one orientation, and the two electrons must be opposite in spin direction; meaning one electron has ms=+1/2 and the other electron has ms=−1/2.

Hund's Rule declares that

the electrons in the orbital are filled up first by electrons whose spins are parallel to each other. Once all the orbitals are filled with unpaired + 1⁄2 spins, the orbitals are then filled with - 1⁄2 spin.