General Chemistry 1 Quarter 2 - Module 1 Quantum Mechanical Description PDF

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NOTGeneral Chemistry 1Quarter 2 - Module 1Quantum Mechanical DescriptionDepartment of Education ● Republic of the Philippines####### Senior High SchoolGeneral Chemistry I- Grade 11 Alternative Delivery M ode Quarter 2 - Module 1: Quantum Mechanical DescriptionFirst Edition, 2020Republic Act 8293, se...

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Senior High School

NOT

General Chemistry 1 Quarter 2 - Module 1 Quantum Mechanical Description

Department of Education ● Republic of the Philippines

General Chemistry I- Grade 11 Alternative Delivery Mode Quarter 2 - Module 1: Quantum Mechanical Description First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalty. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this book are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education – Division of Cagayan de Oro Schools Division Superintendent: Dr. Cherry Mae L. Limbaco, CESO V Development Team of the Module Author:

April Sweet L. Tapayan & Ma. Doris P. Napone

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Senior High School

General Chemistry 1 Quarter 2 - Module 1 Quantum Mechanical Description

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Department of Education ● Republic of the Philippines

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Table of Contents What This Module is About ....................................................................................................................... i What I Need to Know.................................................................................................................................. i How to Learn from this Module .............................................................................................................. .ii Icons of this Module ................................................................................................................................... .ii What I Know ..................................................................................................................................................iii

Quantum Numbers

........................................................................................................ 1

What I Need to Know ................................................................................ 1 What’s New: Fact or Bluff .......................................................................... 1 What Is It .................................................................................................. 2 What’s More: Let’s test your understanding…. .......................................... 4 What’s More: Identify the Orbital ............................................................... 5 What I Have Learned: How much have you learned? ................................ 5 What I Can Do: I am Electroman…. .......................................................... 5 Summary ....................................................................................................................................... ..7 Assessment: (Post-Test) ............................................................................................................. ..8 Key to Answers............................................................................................................................. . 9 References .................................................................................................................................... .12

Module 1 What This Module is About Early efforts by nineteenth-century physicists to comprehend atoms and molecules met with only limited success. With the unwavering pursuit of scientists to come up with different experiments and theories, the flurry of research that ensued altered our concept of nature forever. The use of quantum numbers to describe an electron in an atom is far advantageous to scientists. Since it is very difficult to locate the exact position of an electron in an atom, scientists use different theories and principles in quatum chemistry. Hence, the electron’s location can now be estimated. This module will focus on the discussion about Quantum Numbers. It comprises concepts and activities that will help deepen your understanding of how quantum numbers help in determining the location of an electron in an atom and how it is relevant to our daily lives.

What I Need to Know At the end of this module, you should be able to understand and apply the use of quantum numbers to describe an electron in an atom (STEM_GC11ESIIa-b-54).

i

How to Learn from this Module To achieve the objectives cited above, you are to do the following: •

Take your time reading the lessons carefully.

•

Follow the directions and/or instructions in the activities and exercises diligently.

•

Answer all the given tests and exercises.

Icons of this Module What I Need to

This part contains learning objectives that

Know

are set for you to learn as you go along the module.

What I know

This is an assessment as to your level of knowledge to the subject matter at hand, meant specifically to gauge prior related knowledge. This part connects previous lesson with that

What’s In

of the current one.

What’s New

An introduction of the new lesson through various activities, before it will be presented to you

What is It

These are discussions of the activities as a way to deepen your discovery and understanding of the concept.

What’s More

These are follow-up activities that are intended for you to practice further in order to master the competencies.

What I Have

Activities designed to process what you

Learned

have learned from the lesson

What I can do

These are tasks that are designed to showcase your skills and knowledge gained, and applied into real-life concerns and situations.

ii

What I Know

Pretest: MULTIPLE CHOICE: Directions: Read and understand each item and choose the letter of the correct answer. Write your answers on a separate sheet of paper. 1. What do you call the three-dimensional orientation of the orbital in space around the nucleus? A. magnetic quantum number B. principal quantum number

C. electron configuration D. geometry

2. Which quantum number indicates the relative size of an orbital? A. magnetic quantum number C. electron configuration B. principal quantum number D. geometry 3. Who are the founding fathers of Quantum Mechanics? A. Werner Karl Heisenberg C. Isaac Newton B. Erwin Schrodinger D. A & B 4. Which of the following combinations is allowed? A. n=2, ℓ =1, ml= -1, ms= +1/2 C. n=3, ℓ =1, ml=-3, ms= -1/2 B. n=1, ℓ =1, ml= +1, ms= -1/2 D. None of the above 5. Who said that no two electrons can have the same set of four quantum numbers? A. Heisenberg C. Hund B. Einstein D. Pauli 6. Which of the following symbolizes the spin of an electron? A. mℓ C. n B. ms D. ℓ 7. How many types of quantum numbers? A. 6 B. 2

C. 8 D. 4

8. What does the magnetic quantum number describe? A. distance of the most electron-dense C. number of electron B. spatial orientation of the orbital D. shape of orbital 9. Heisenberg’s Uncertainty Principle states that the___ and ___ of an electron cannot be known simultaneously. How does this statement be completed correctly? A. position, momentum C. position, charge B. momentum, speed D. position, mass 10. What does the quantum mechanical model describes electrons? A. particles with wave-like properties C. particles B. small, hard spheres D. waves iii

What I Need to Know In your previous lesson, you were taught about subatomic particles or the composition of an atom. They are the proton and neutron that are located inside, and the electron that is located outside the nucleus. In this lesson, we will be focusing on the characteristics of an electron since it has an important role in chemical bonding. Since the electron is located outside the nucleus, it is difficult to determine its exact location. That is why we have to learn about the behaviors of quantum particles. Of these behaviors, the most we can do is to calculate probabilities as to the location and behavior of the particles. Bohr’s model of the hydrogen atom suggests that the electron orbits the nucleus like our solar system (e.g. the planets around the sun). However, the quantum mechanical description of the hydrogen atom has proven that Bohr’s model of electrons is incorrect. It states that we do not know exactly where the electron is, but with high probability, we can conclude that the electron is most likely to be found in an orbital (Chang, 2010). In this lesson, you should be able to describe the electrons (e-) in orbitals using the four quantum numbers.

Figure 1. Bohr’s Model (Electron in orbit)

Figure 2. Quantum Mechanics (Electron in orbital)

According to Heisenberg’s uncertainty principle, it is impossible to determine both the energy and position of an electron at the same time. Thus, as we know more about the electron’s energy, we know less about its position and vice versa.

What’s New Activity 1: Fact or Bluff Directions: Carefully read the following statements below and write FACT if it is TRUE and BLUFF if it is FALSE on the space provided on the left side. _______1. The quantum mechanical description of the electron is more accurate than that of Bohr’s model. _______2. No two electrons have the same 4 quantum numbers. _______3. We can both know the energy and the position of electrons at the same time. _______4. Any two electrons in the same orbital must have the same spins. _______5. The four quantum numbers are used to describe the probable location of an electron in an atom. 1

GUIDE QUESTION: What is the difference between Bohr’s model and the quantum mechanical model of an electron? State your answer in 3-5 sentences only.

What Is It To describe the orbitals in which electrons can be found, quantum numbers are required. Quantum numbers are a set of values that give us information about the location of electrons in the electron cloud of an atom. It can be used to determine the electron configuration of an atom. According to the Pauli Exclusion Principle, each electron in an atom has an exclusive set of quantum numbers and no two electrons can have the same combination of four quantum numbers. To fully characterize the movement and trajectories of each electron within an atom, four quantum numbers are used. A wave function that obeys the Schrödinger equation describes the combination of all quantum numbers of all electrons in an atom. Each electron in an atom has its own set of quantum numbers, and no two electrons may have the same four quantum numbers, according to the Pauli Exclusion Principle. Quantum numbers are essential because they may be used to figure out an atom's electron configuration and where its electrons are most likely to be found. Other properties of atoms, such as ionization energy and atomic radius, are also understood using quantum numbers. The main quantum number (n), the orbital angular momentum quantum number (l), the magnetic quantum number (ml), and the electron spin quantum number (ms) are the four quantum numbers found in atoms. The energy of an electron and the most likely distance of the electron from the nucleus are described by the primary quantum number, (n). In other terms, it relates to the size of an electron's orbital and the energy level it occupies. The form of the orbital is described by the number of subshells (l) (Silberberg, 2013).

The Four Quantum Numbers Table 1. Quantum numbers and their possible values

Quantum Number Symbol Possible Values Principal Quantum Number n 1,2,3,4… (positive integers) Angular Momentum Quantum Number ℓ 0,1,2,3… (0 to n-1) Magnetic Quantum Number ml - ℓ,…-1,0,1…,+ ℓ Spin Quantum Number ms +1/2, -1/2 1. Principal Quantum Number The principal quantum number (n), describes the energy of an electron. It refers to the energy level and the size of the orbital an electron is likely to be found. The value of n starts from 1 to the shell containing the outermost electron of that atom. The larger the value of (n), the greater is the energy and the larger is the orbital. The group of 2

orbitals with the same value of n is called an electron shell. All the orbitals that have n = 2, for example, are said to be in the second shell. Carbon is in the second period of the periodic table, so, its outermost electron is in the shell with an energy level of 2. Therefore, an electron in Carbon can have an (n) value from 1 to 2. 2. Angular/Azimuthal Quantum Number In chemistry, the angular quantum number (ℓ), defines the shape of an atomic orbital. It also strongly influences bond angles and chemical bonds. It is defined in chemistry that if ℓ = 0, it is called an s orbital, ℓ = 1 is a p orbital, ℓ = 2 a d orbital, and ℓ = 3 an f orbital. The first p orbital (ℓ = 1) is in the second electron shell (n = 2), the first d orbital (ℓ = 2) is in the third shell (n = 3), and so on. The set of orbitals that have the same n and l values is called a subshell. 3. Magnetic Quantum Number The magnetic quantum number (ml), describes the orientation of the orbital in space and can have integral values between - ℓ and ℓ, including zero. For example, the p subshell (ℓ = 1) contains three orbitals, so the ml of an electron in a p subshell will be −1, 0, or 1. The outermost electron of Carbon is in a 2p subshell. This means that for that electron, n=2 and ℓ = 1. Since ℓ = 1, we can conclude that there are three 2p orbitals in this subshell because there are three values of (ml), given by -1, 0, and 1. 4. Spin Quantum Number Individual electrons within an orbital has a property represented by the spin quantum number. Each orbital may hold up to two electrons with opposite spin directions. Electrons are not spinning in a physical sense, this is just a representation of the idea that there are two possible values for the spin quantum number. When an electron is assigned to spin up, it is represented by an upward arrow and a value of +1/2. If an electron is spinning down, it is represented by a downward arrow and a value of -1/2 (Brown, 2015).

Figure 3. Representation of the Spin Quantum Number values

The following are the principles and rule involved in quantum mechanics: (These will be elaborated in the next module) 3

Pauli Exclusion Principle: Wolfgang Pauli established in 1926 that a set of quantum numbers is unique to a single electron. That is to say, no two electrons can have the same n, l, ml, or ms values. The first three quantum numbers identify a specific orbital and can have the same values, but the fourth is important and must have opposite spins. Hund's Rule: When orbitals belong to the same primary shell, their energy levels may be the same. These orbitals are referred to be degenerate, or "equal energy," orbitals. Electrons fill orbitals one at a time, according to Hund's Rule. This means that when using the arrow model to design electron configurations, you must first fill each shell with one electron before starting to pair them up. Remember that an electron has a negative charge and that electrons repel each other. By remaining unpaired, electrons will attempt to establish distance between themselves and other electrons. This also explains why electrons in orbitals have opposite spins (i.e. and ). Heisenberg Uncertainty Principle: This principle states that we cannot accurately measure an electron's momentum and position at the same time. The position of the electron gets less certain as the electron's momentum becomes more certain, and vice versa (Silberberg, 2013).

What’s More (A) Activity 2.1: Let’s test your understanding! Directions: Answer the following questions below as directed on a separate sheet of paper and submit it to your teacher as soon as you are finished. 1. List the values of n, ℓ, and m/ for orbitals in the 4d subshell. n value/s

ℓ value/s

ml value/s

2. What is the total number of orbitals associated with the principal quantum number n=3? Defend your answer. For items 3-5, identify if the following set of quantum numbers are correct. If not, indicate which quantum number is wrong. 3. n=2, ℓ =1, ml= -1, ms= +1/2 4. n=3, ℓ =1, ml=-3, ms= -1/2 5. n=1, ℓ =1, ml= +1, ms= -1/2

What’s More (B) Activity 2.2: Identify the orbital 4

Directions: Determine which orbital is described by the following sets of quantum numbers. If the set includes an incorrect value, write “not allowed”. n ℓ ml Orbital Number 2 1 -1 2p (example) 1. 2. 3.

1 3 3

0 -3 2

0 2 -2

4. 5. 6.

2 0 4

0 0 2

-1 0 1

What Have I Learned Activity 3: How much have you learned? Directions: In your own words, describe the following terms in 2-3 sentences only. 1. Quantum Number 2. Principal Quantum Number

3. Angular Quantum Number 4. Magnetic Quantum Number

What I Can Do Activity 4: I am ELECTRON MAN! Directions: Imagine yourself as an electron. Like an electron, you should keep track of your location and activity for three days. If quantum numbers give information about the location of an electron or set of electrons, you could describe your location in any number of ways (e.g. GPS coordinates, qualitatively describing your surroundings, google map, etc.). Fill out the table below with the needed details and answer the questions that follow. The first row serves as an example. Electron Name: Day

Time

1

9:00 AM

1

9:00 AM

1

3:00 PM

1

7:00 PM

2

9:00 AM

2

3:00 PM

Special Skill: Location Dining Area, Rizal’s House, Cagayan de Oro City, Philippines

5

Activity Having breakfast with family

2

7:00 PM

3

9:00 AM

3

3:00 PM

3

7:00 PM

Follow-up Questions: 1. What is the importance of understanding the role of quant...