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2.8 - Exercises

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Atomic Structure Fundamentals

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Teacher
Teacher

Today, we are going to revisit the fundamentals of atomic structure. What are the three main subatomic particles that compose an atom?

Student 1
Student 1

Electrons, protons, and neutrons!

Teacher
Teacher

Correct! Can anyone tell me the charge associated with each of these particles?

Student 2
Student 2

Electrons are negatively charged, protons are positively charged, and neutrons have no charge.

Teacher
Teacher

Exactly! To remember this, think of 'E for Electron - Negative', 'P for Proton - Positive', and 'N for Neutron - Neutral'. Let's recap what we learned about their masses. Who can share those?

Student 3
Student 3

An electron is very light compared to protons and neutrons, which are similar in mass.

Teacher
Teacher

Great! So, while the electron's mass is about 1/1836 of a proton or neutron, does this mean protons and neutrons are heavier?

Student 4
Student 4

Yes! They each weigh about 1 amu, or atomic mass unit, which is significant compared to the mass of electrons.

Teacher
Teacher

Excellent discussion! The key here is understanding the roles of these particles in the properties of elements. So, what defines the identity of an atom?

Student 1
Student 1

The number of protons in its nucleus!

Teacher
Teacher

Correct! And that brings us to the concept of atomic number, which is crucial for understanding the periodic table.

Quantum Numbers and Electron Configurations

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Teacher
Teacher

Now let's discuss electron configurations and the role of quantum numbers. Who can remind me what quantum numbers are?

Student 2
Student 2

They are numbers that describe the size, shape, and orientation of orbitals and the spin of the electrons!

Teacher
Teacher

Exactly! Can anyone list the four quantum numbers we use?

Student 3
Student 3

They are the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms).

Teacher
Teacher

Well done! For the principal quantum number, n, how does it affect orbital energy?

Student 4
Student 4

As n increases, the energy increases and the electron is found farther from the nucleus.

Teacher
Teacher

Yes, and what about l? What shape does it define?

Student 1
Student 1

It defines the shape of the orbital, such as s, p, d, or f.

Teacher
Teacher

Correct! Remember 's' for spherical shapes, 'p' for dumbbell-shaped, and 'd' for cloverleaf. Lastly, how do we denote electron configurations?

Student 2
Student 2

Using notation like 1s2 2s2 2p6... for the arrangement of electrons.

Teacher
Teacher

Exactly! You’ve mastered this topic. Always remember to account for all quantum numbers when figuring out an element's electronic structure.

Calculations and Applications

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Teacher
Teacher

For our last session today, we'll do some calculations based on atomic theory. Let's start with a simple exercise. How many electrons are in one mole of electrons?

Student 3
Student 3

That would be Avogadro's number, 6.022 × 10^23 electrons.

Teacher
Teacher

Great! Next, if we wanted to find the total mass of these electrons, how would we compute it?

Student 1
Student 1

I'll use the mass of one electron, which is about 9.11 × 10^–31 kg, and multiply it by Avogadro's number.

Teacher
Teacher

Correct! What's the mass of a mole of electrons then?

Student 4
Student 4

It's approximately 5.4859 × 10^–4 kg.

Teacher
Teacher

Excellent work! Now, let’s try a more challenging problem. If you were to calculate the wavelength of light emitted during a transition from n = 3 to n = 2 in the hydrogen atom, what would you begin with?

Student 2
Student 2

I would use the Rydberg formula to find the wavelength based on the respective energy levels.

Teacher
Teacher

That's right! Remember the formula and let’s have you calculate it. Keep in mind the principles of transition energy as well.

Student 3
Student 3

After applying the Rydberg formula, we get a wavelength of around 656 nm.

Teacher
Teacher

Fantastic! That color corresponds to red light in the spectrum, showing how important this concept is. Well done!

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

This section provides various exercises related to atomic structure, covering concepts from atomic particles to quantum numbers and electron configurations.

Standard

In this section, exercises are designed to reinforce understanding of atomic structure, including the properties of electrons, protons, and neutrons, as well as the application of quantum numbers in electronic configurations. The exercises encourage critical thinking and practical application of theoretical concepts.

Detailed

Detailed Summary

The section 'Exercises' serves as a comprehensive tool to reinforce learning about atomic structure and quantum mechanics. It includes practical problems that challenge students to apply their knowledge of atomic particles—specifically, electrons, protons, and neutrons. Additionally, students engage with exercises that require the utilization of quantum numbers to describe electron configurations.

This section emphasizes the transition from theoretical knowledge to practical application through well-structured exercises ranging from easy computation problems to complex conceptual questions. Activities include calculating the number of electrons in a mole, identifying isotopes, or calculating wavelengths and energies based on quantum principles.

Each exercise is aimed at facilitating engagement with core concepts established in atomic theory, helping students critically think about the nature of matter at the atomic level. This culminates in a deeper understanding of the underlying principles that govern atomic behavior and the intricate details of electron organization within atoms.

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Audio Book

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Exercise 2.1

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(i) Calculate the number of electrons which will together weigh one gram.
(ii) Calculate the mass and charge of one mole of electrons.

Detailed Explanation

In this exercise, you are tasked with determining certain quantities related to electrons. For part (i), you need to use the mass of a single electron (approximately 9.11 × 10^-31 kg) to calculate how many of them together would weigh one gram (1 g = 0.001 kg). For part (ii), recall that one mole of any substance contains Avogadro's number of particles (approximately 6.022 × 10^23). Knowing the charge of an electron is -1.602 × 10^-19 C, you can calculate the total charge of one mole of electrons as well.

Examples & Analogies

Think of this calculation like trying to figure out how many grains of sand it would take to weigh a specific weight, like a small bag. Each grain represents an electron, and just as you can count grains of sand, you can count electrons in terms of their mass and charge.

Exercise 2.2

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(i) Calculate the total number of electrons present in one mole of methane.
(ii) Find (a) the total number and (b) the total mass of neutrons in 7 mg of 14C. (Assume that mass of a neutron = 1.675 × 10–27 kg).
(iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH3 at STP. Will the answer change if the temperature and pressure are changed?

Detailed Explanation

For (i), methane (CH₄) has one carbon atom and four hydrogen atoms, leading to a total of 5 electrons. Since we have one mole of methane, we simply multiply the total number of electrons by Avogadro's number. For (ii), carbon-14 (14C) has 6 protons and 8 neutrons. Calculate the total number of neutrons and then multiply by their mass to find the total mass of neutrons. For (iii), NH₃ has 1 nitrogen and 3 hydrogens, resulting in 7 protons in total; calculate the number and mass based on the mentioned average proton mass. The last question considers how changes in temperature and pressure at STP affect the mass of the substance, which remains constant regardless of these environmental conditions.

Examples & Analogies

Think of electrons in molecules akin to guests at a party. In a mole of methane, each guest represents an electron. When you count all the guests, you multiply by how many parties you've got (or moles). Similarly, the neutron and proton calculations are like counting people and their weights. Whether the party is held outside in the sun or in a basement doesn’t change how many guests you have or how much total weight they bring!

Exercise 2.3

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How many neutrons and protons are there in the following nuclei?
613CO Mg Fe Sr

Detailed Explanation

For each nucleus given, you should look at the atomic number (Z) and the mass number (A). The mass number indicates the total number of protons and neutrons in the nucleus. By knowing the atomic number (which tells you the number of protons), you can easily find the number of neutrons using the formula: neutrons = mass number - atomic number. Apply this method for carbon-13, magnesium, iron, and strontium respectively to find the number of protons and neutrons in each case.

Examples & Analogies

Think of this as a fruit basket where each type of fruit has a specific total count (mass number), and you know how many apples (protons) are in the basket by the 'fruit count label' (atomic number). To find out how many of other fruits (neutrons) there are, you subtract the apples from the total fruit count!

Exercise 2.4

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Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A).
(i) Z = 17, A = 35.
(ii) Z = 92, A = 233.
(iii) Z = 4, A = 9.

Detailed Explanation

The complete symbol for an atom is written using the format AZX, where A is the mass number and Z is the atomic number. For example, for Z = 17 and A = 35, the symbol would be written as 35717Cl for chlorine. Repeat this process for the other atoms, ensuring to correctly identify the element's chemical symbol as well.

Examples & Analogies

Imagine you're labeling boxes of supplies. The 'Z' is the label telling you how many types of items you have (protons), while 'A' tells you the total number of items, including all types. When you fill out the label for each box, it’s like writing down how many items and their total for easy identification!

Exercise 2.5

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Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wavenumber ( ) of the yellow light.

Detailed Explanation

To calculate the frequency, use the formula ν = c/λ, where c is the speed of light (approximately 3.00 x 10^8 m/s) and λ is the wavelength in meters. After finding the frequency, you can find the wavenumber by using the formula k = 1/λ, where λ is in meters. Ensure to convert the wavelength from nanometers to meters for accurate calculations.

Examples & Analogies

Think of this task as tuning a radio. Each frequency corresponds to a station (wavelength), and calculating the frequency from the wavelength is like tuning the dial until you find the right station. The wavenumber gives you a shorthand notation of how 'tight' or 'loose' the waves are, sort of like adjusting the volume of that radio to get the sound just right!

Exercise 2.6

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Find energy of each of the photons which correspond to light of frequency 3×1015 Hz.
(ii) have wavelength of 0.50 Å.

Detailed Explanation

For each part, use the equation E = hν for the first part, where h (Planck’s constant) is approximately 6.626 x 10^-34 J·s. For the second part, convert the wavelength from Ångström units to meters and use the equation E = hc/λ to find the energy. Note that it's important to use proper conversion for accurate results.

Examples & Analogies

Consider this as determining how much 'energy' each sip of a drink provides. If the drink is consistent in how it energizes you (like a photon corresponds to a specific frequency or wavelength), calculating using these formulas gives you the exact boost you get from each sip!

Exercise 2.7

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Calculate the wavelength, frequency and wavenumber of a light wave whose period is 2.0 × 10–10 s.

Detailed Explanation

Start by calculating the frequency using the formula ν = 1/T, where T is the period. Once you've determined the frequency, apply ν = c/λ to find the wavelength. Finally, calculate the wavenumber using the equation k = 1/λ. Remember to convert units where necessary.

Examples & Analogies

Imagine you're timing how long a musical note is played (the period). If you know how often it plays in a minute (frequency), you can find how 'long' the sound travels (wavelength). Each calculation is like mapping out how music travels through the air!

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Atomic structure: Comprised of protons, neutrons, and electrons.

  • Quantum numbers: Describe electron arrangement; include n, l, ml, and ms.

  • Electron configuration: Notation representing the distribution of electrons in orbitals.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Example of calculating the total number of electrons in one mole leads to Avogadro's number.

  • Using Rydberg's formula to calculate wavelengths of transitions in hydrogen.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • Electrons go and flow, negatively they show!

🎯 Super Acronyms

PAN for Protons (Positive), Electrons (Negative), and Neutrons (Neutral).

📖 Fascinating Stories

  • Imagine a tiny kingdom inside an atom where Protons are the kings, Neutrons are the strong guards, and Electrons are the wandering subjects.

🧠 Other Memory Gems

  • PEAN – Protons are Positive, Electrons are Negative, Neutrons are Neutral.

Flash Cards

Review key concepts with flashcards.

Glossary of Terms

Review the Definitions for terms.

  • Term: Atomic Structure

    Definition:

    The arrangement and organization of protons, neutrons, and electrons in an atom.

  • Term: Quantum Numbers

    Definition:

    A set of four numbers that describe the energy level, shape, and orientation of orbitals, and the spin of electrons.

  • Term: Electron Configuration

    Definition:

    The distribution of electrons in an atom's orbitals.

  • Term: Avogadro's Number

    Definition:

    The number of particles (atoms, molecules, etc.) in one mole of a substance, approximately 6.022 × 10^23.