Name: finding rate law from initial rates
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 53 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.7

IPC.7.F

Determining Order of Reaction

화학 반응의 경우 속도 법칙은 반응 속도와 반응물 농도 사이의 관계를 나타냅니다. 반응물 농도의 지수는 반응 속도에 개별적으로 영향을 미치며 이것을 반응 차수라고 합니다. 반응 차수는 화학 반응을 다양한 반응물의 농도에 대해 여러 번 반복하여 초기 반응 속도를 측정하는 초기 속도 방법을 사용하여 실험적으로 결정됩니다.

반응물 농도가 증가하면 반응 속도가 선형적으로 비례하여 증가하므로 1차 반응의 특징을 가집니다. 반응물의 농도를 두 배로 증가시키면 초기 속도가 네 배로 증가하며 따라서 2차 반응으로 관찰할 수 있습니다. 그러나 반응물 농도의 변화가 초기 속도 값에 영향을 미치지 않으면 0차 반응으로 관찰할 수 있습니다.

초기 속도에 대한 데이터가 초기 반응물 농도의 변화와 해당 속도 사이에 신뢰할 수 없는 관계를 나타내는 경우, 속도 법칙에 대한 비율을 계산합니다. 여기서 반응물의 두 농도 값과 반응 속도를 사용하여 반응 차수를 결정합니다. 하지만 다중 반응물과의 반응은 어떨까요?

먼저 초기 속도 방법을 사용하여 각 반응물의 반응 차수를 개별적으로 결정합니다. 다음 개별적인 반응 차수는 속도 법칙을 공식화하는 각각의 반응물 농도에 대한 지수로 표현됩니다. 마지막으로 속도 법칙의 개별 지수의 합으로 전체 반응 차수를 결정합니다.

반응 차수는 반응물 농도에 대한 반응 속도의 의존성을 나타내지만 상대 반응 속도에 대한 직접 측정값은 속도 상수로 표시됩니다. 속도 상수 k는 반응속도와 반응물 농도의 적과 관련된 비례 계수입니다. 속도 상수의 단위는 전체 반응 차수에 따라 달라지며 속도 상수에 대해 해결할 속도 법칙을 재배열하여 결정할 수 있습니다.

0차 반응의 경우 k는 초당 단위 몰농도를 가집니다. 1차 반응의 단위는 1/s 이고 2차 반응의 단위는 1/mol-s 입니다. 속도 상수가 크면 반응이 빠르다는 것을 나타냅니다.

반대로 속도 상수가 작으면 반응이 느리다는 것을 나타냅니다. 0 값은 화학 반응이 없음을 나타냅니다.

반응 순서 결정

속도 법칙은 화학 반응 속도와 반응물의 농도 사이의 관계를 설명합니다. 속도 법칙에서는 반응물의 농도가 변함에 따라 반응 속도가 어떻게 변하는지 관찰하여 속도 상수 k와 반응 차수를 실험적으로 결정합니다. 비율 법칙을 결정하는 일반적인 실험적 접근 방식은 초기 비율 방법입니다. 이 방법에는 다양한 초기 반응물 농도를 사용하여 수행된 여러 실험 시도에 대한 반응 속도를 측정하는 작업이 포함됩니다. 이러한 시도에 대해 측정된 속도를 비교하면 반응 차수를 결정할 수 있으며, 이어서 속도 법칙을 공식화하는 데 함께 사용되는 속도 상수를 결정할 수 있습니다.

예를 들어, 오존과 반응하는 산화질소 [NO (g) + O^3 (g) ⟶ NO_2 (g) + O^2 (g)]가 포함된 반응 속도는 실험실에서 초기 속도법의 실험 자료를 통해 결정할 수 있습니다.

<div class="overflow">
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">평가판 </td>
			<td style="color: black; border: 1px solid black; text-align: center;">【아니오】 (몰/L)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">[O3] (몰/L)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Δ[NO2]/Δ t(몰/L/s)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10-6 </td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.00 × 10-6 </td>
			<td style="color: black; border: 1px solid black; text-align: center;">6.60 × 10-5 </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">2</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">6.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.32 × 10-4</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.98 × 10-4</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">4</td>
			<td style="color: black; border: 1px solid black; text-align: center;">2.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.96 × 10-4</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">9.00 × 10-6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">5.94 × 10-4</td>
		</tr>
	</tbody>
</table>
</div>

요율 자료에서 일반적인 요율 법칙; 속도 = k[NO]^m[O_3]^n이 공식화됩니다. 반응 차수 m과 n의 값과 속도 상수 k는 세 부분으로 구성된 프로세스를 사용하여 실험 자료로부터 결정됩니다.

1 단계에서는 [NO]가 변하고 [O_3]가 일정한 자료로부터 m의 값이 결정됩니다. 실험 3, 4, 5에서 [NO]는 변화하는 반면 [O_3]는 일정하게 유지됩니다. [NO]가 시험 3에서 4로 두 배로 증가하면 비율이 두 배로 증가하고, [NO]가 시험 3에서 5로 3배로 증가하면 비율도 세 배로 증가합니다. 따라서 비율도 [NO]에 정비례하고 비율 법칙에서 m은 1과 같습니다.

2단계에서는 [O_3]가 변하고 [NO]가 일정한 자료로부터 n의 값이 결정됩니다. 실험 1, 2, 3에서 [NO]는 일정하고 [O_3]는 다양합니다. 반응 속도는 [O_3]의 변화에 정비례하여 변화합니다. [O_3]가 실험 1에서 2로 두 배가 되면 비율도 두 배가 됩니다. [O_3]가 실험 1에서 3으로 3배 증가하면 속도도 3배 증가합니다. 따라서 속도는 [O_3]에 정비례하고 n은 1과 같습니다. 속도 법칙은 다음과 같습니다. 속도 = k [NO]^1 [O_3]^1 = k [NO][O_3]

3단계에서 k 값은 한 세트의 농도(예: 시험 1의 자료)와 해당 비율로부터 결정됩니다.

<img alt="Eq1" src="/files/ftp_upload/11376/11376_Equation 1.png" style="text-align: center; height: 145px;" />

초기 속도 방법의 자료가 초기 농도와 초기 속도 사이의 관계를 직접적으로 암시하지 않는 반응에서는 속도 법칙의 비율을 포함하는 계산을 사용하여 반응 차수와 속도 상수를 계산할 수 있습니다.

예를 들어, 반응 2 NO(g) + Cl_2(g) ⟶ 2 NOCl(g)에 대한 일반 속도 법칙은 속도 = k [NO]^m [Cl_2]^n으로 표현됩니다.

초기 요율 방법의 자료는 다음과 같습니다.

<div class="overflow">
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">평가판 </td>
			<td style="color: black; border: 1px solid black; text-align: center;">【아니오】 (몰/L) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">[Cl2] (몰/L) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">초기 요금(mol/L·s) </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.00300</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">2</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.15</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.00450</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.15</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.10</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.00675</td>
		</tr>
	</tbody>
</table>
</div>

m과 n의 값은 대수적 접근법을 사용하여 실험 자료로부터 결정될 수 있으며, 그에 따라 k의 값이 결정됩니다.

1단계에서는 [NO]가 변하고 [Cl_2]가 일정한 자료로부터 m의 값이 결정됩니다. 비율 법칙의 비율은 두 가지 다른 시행(예: 시행 3 및 시행 1)의 자료를 대체하여 표현됩니다.

<img alt="Eq2" src="/files/ftp_upload/11376/11376_Equation 2.png" style="text-align: center; height: 260px;" />

2단계에서는 [Cl_2]가 변하고 [NO]가 일정한 자료로부터 n의 값이 결정됩니다.

<img alt="Eq4" src="/files/ftp_upload/11376/11376_Equation 4.png" style="text-align: center; height: 120px;" />

m과 n의 계산된 값을 사용하여 속도 법칙은 속도 = k [NO]_2 [Cl_2]로 표현됩니다.

3단계에서는 속도 상수 k의 수치가 적절한 단위로 결정됩니다. 반응 속도의 단위는 mol/L·s입니다. k의 단위는 속도법칙의 다른 모든 매개변수의 단위를 대체하여 결론지어집니다. 이 예에서 농도 단위는 mol^3/L^3입니다. k의 단위는 L^2/mol^2·s여야 하며 속도는 mol/L·s로 표시됩니다. k 값은 비율 법칙 표현식이 해결되면 임의의 실험 시행(예: 시행 1)의 값을 간단히 대체하여 결정됩니다.

<img alt="Eq5" src="/files/ftp_upload/11376/11376_Equation 5.png" style="text-align: center; height: 70px;" />

반응 순서 및 속도 상수 단위

일부 반응에서는 속도 법칙의 반응 차수가 해당 반응의 화학 반응식의 계수와 동일합니다. 이것은 단지 우연일 뿐이며 그렇지 않은 경우도 많습니다. 속도 법칙은 일부 반응물에 대해 분수 차수를 나타낼 수 있으며, 한 반응물의 농도가 증가하면 반응 속도가 감소할 때 음의 반응 차수가 때때로 관찰됩니다. 속도 법칙은 실험에 의해서만 결정되며 반응 화학량론으로는 확실하게 예측할 수 없습니다.

속도 상수의 단위는 반응의 전체 순서를 수용하기 위해 적절하게 변경됩니다. 0차 반응의 속도 상수 단위는 mol/L·s(또는 M/s)이고 1차 반응의 속도 상수 단위는 1/s입니다. 2차 반응의 속도상수의 단위는 L/mol·s(또는 1/M·s)이고 3차 반응의 속도상수의 단위는 L^2/mol^2·s입니다. 농도와 시간의 특정 단위는 (mol/L)과 (s)로 표시되지만, 농도와 시간의 특성을 나타내기 위해 다른 유효한 단위를 사용할 수도 있습니다.

이 문서는 에서 발췌되었습니다 <a href="https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws#57033">Openstax, Chemistry 2e, Section 12.3: Rate Laws.</a>

속도 법칙은 화학 반응 속도와 반응 물질의 농도 사이의 관계를 설명합니다. 비율 법칙에서, 비율 상수 k 및 ...

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화학

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Chemical Kinetics

화학 반응 속도론

KEY TERMS AND CONCEPTS

주요 용어 및 개념

finding rate law from initial rates

Rate laws connect the speed of a chemical reaction to the concentration of its reactants. The rate constant, k, and the reaction orders are not taken from the chemical equation. They are found experimentally by watching how the rate changes when the reactant concentrations change.

One common way to do this is the method of initial rates. In this method, several trials are run with different starting concentrations. The measured rates are then compared to determine the reaction orders and, after that, the rate constant. These values are used to write the rate law.

For the reaction of nitric oxide with ozone, NO(g) + O3(g) → NO2(g) + O2(g), the data show how this works in the lab. When [NO] is held constant and [O3] changes, the rate changes in the same way. When [O3] doubles, the rate doubles. When [O3] triples, the rate triples. This shows that the reaction is first order in O3. A similar comparison using trials where [O3] stays constant shows that the rate is also directly proportional to [NO], so the reaction is first order in NO as well. The rate law is therefore rate = k[NO][O3].

In other reactions, the orders are found with an algebraic ratio of rate laws. For the reaction 2 NO(g) + Cl2(g) → 2 NOCl(g), the rate law is written as rate = k[NO]m[Cl2]n. Using the trial data, one step gives m = 2 and another gives n = 1. The rate law becomes rate = k[NO]2[Cl2]. The value of k is then found by using one trial and solving for the constant.

The units of the rate constant depend on the overall order of the reaction. Rate is measured in mol/L·s, and the units for k must match the rate law. For this example, the concentration terms give mol3/L3, so k must have units of L2/mol2·s. In general, a zero-order reaction has k in mol/L·s, a first-order reaction has k in 1/s, a second-order reaction has k in L/mol·s, and a third-order reaction has k in L2/mol2·s.

Reaction order does not always match the coefficients in the balanced equation. That match can happen, but it is only a coincidence. Rate laws can also include fractional orders, and some reactants can have negative orders if a higher concentration lowers the reaction rate. Because of this, rate laws are determined by experiment, not by stoichiometry. Although the examples here use mol/L and s, other valid concentration and time units can also be used.

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reaction mechanisms

Elementary Steps in Reaction Mechanisms

Chemical reactions can happen in steps, and a balanced equation does not show the full path at the molecular level. A reaction mechanism, also called a reaction path, gives the step-by-step process that explains how reactants become products. The decomposition of ozone is one example of a reaction that can be described by a sequence of steps. Each step in a mechanism is an elementary reaction. These elementary reactions happen in order, and when they are added together, they give the balanced...

rate-determining steps

Reaction Bottlenecks in Chemical Kinetics

Reaction bottlenecks help explain rate-determining steps in multistep reaction mechanisms. In a mechanism with several elementary steps, one step is often much slower than the others. That slowest step is called the rate-limiting step, or rate-determining step. A reaction cannot move faster than its slowest step, so this step controls the overall reaction rate. The idea is like traffic on a four-lane freeway with one lane closed. Cars can only move as fast as the bottleneck allows. In the same...

catalysis

Catalyst Action in Reaction Rates

Catalysts change the rate of a chemical reaction by giving it a faster path. A catalyst increases reaction rate without being consumed during the process. Its effect is often explained with reaction mechanisms and energy diagrams. For an endothermic reaction, the reactants and products start and end at the same energies in both cases. The uncatalyzed path is a one-step mechanism with one transition state. The catalyzed path follows a different mechanism with two transition states and a lower...

enzymes

Enzyme Action and Inhibition

Enzymes are biological catalysts that speed up many reactions in living organisms. They help control cellular metabolism by lowering the activation energy needed for biochemical reactions. When activation energy drops, reaction rates can increase. Enzyme problems can also lead to serious disease. A genetic abnormality that causes G6PD, or glucose-6-phosphate dehydrogenase, deficiency can disrupt the pathway that supplies NADPH to cells. In red blood cells, this can reduce glutathione and...

key terms and concepts

Use initial-rate data to find reaction order and the rate constant. Explore examples with NO, ozone, and NOCl, plus how rate constant units change.

Finding Rate Law from Initial Rates | JoVE K12

chemistry

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north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Matter and its Interactions

PS.Chm.5.1

Pennsylvania State Academic Standards

Physical Science

Chemical Reactions

3.2.9-12.D

3.2.9-12.E

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

Virginia  Standards of Learning

HIgh School

CH.7

CH.7.e

Next Generation Science Standards

Matter and Its Interactions

HS-PS1-4

HS-PS1-5

Florida Department of Education

SC.912.P.12

SC.912.P.12.12

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-5.

The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

Subatomic Particles

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller ...

Elements: Chemical Symbols and Isotopes

A chemical symbol is an abbreviation used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. The same symbol is ...

Ions and Ionic Charges

In ordinary chemical reactions, the nucleus &mdash; which contains the protons and neutrons of each atom and thus identifies the element &mdash; remains ...

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Atomic Mass

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

Molar Mass

The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example, ...

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

Types of Chemical Bonds

Chemical bonding theories were pioneered by American chemist Gilbert&#xA0;N. Lewis. He developed a model called the Lewis model to explain the type and ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

The Born-Haber Cycle

Lattice Energy&#xA0;

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a ...

trends-in-lattice-energy-ion-size-and-charge

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure ...

Covalent Bonding and Lewis Structures

Compared to ionic bonds, which results from the transfer of electrons between metallic and nonmetallic atoms, covalent bonds result from the mutual ...

Electronegativity

Whether a bond is nonpolar or polar covalent is determined by a property of the bonding atoms called electronegativity.&#xA0;

Electronegativity values of ...

bond-polarity-dipole-moment-and-percent-ionic-character

Bond Polarity, Dipole Moment, and Percent Ionic Character

Bond Polarity

The absolute value of the difference in electronegativity (&Delta;EN) of two bonded atoms provides a rough measure of the polarity to be ...

lewis-structures-of-molecular-compounds-and-polyatomic-ions

Lewis Structures of Molecular Compounds and Polyatomic Ions

To draw Lewis structures for complicated molecules and molecular ions, it is helpful to follow a step-by-step procedure as outlined:


	Determine the ...

Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

Bonding in Metals

Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Dr&#xFC;de called the ...

Model basic atomic structure and relate an element's atomic structure to its bonding, reactivity, and placement on the Periodic Table.

IPC.7.A

physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

The characteristics that enable us to distinguish one substance from another are called properties.

Physical Properties of Matter

A physical property is ...

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

Ionic Radii

Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it ...

Ionization Energy

The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy ...

Electron Affinity

The electron affinity (EA) is the energy change for adding an electron to a gaseous atom to form an anion (negative ion).



This process can be either ...

Alkali Metals

Group 1 elements are soft and shiny metallic solids. They are malleable, ductile, and good conductors of heat and electricity. The melting points of the ...

Halogens

Group 17 elements, known as halogens, are nonmetals. At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine a solid. ...

Noble Gases


The elements in group 18 are noble gases (helium, neon, argon, krypton, xenon, and radon). They earned the name &ldquo;noble&rdquo; because they were ...

Use patterns within the Periodic Table to predict the relative physical and chemical properties of elements.

IPC.7.B

Classifying Matter by State

Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, ...

Classifying Matter by Composition

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories &mdash; pure substances and ...

Phase Transitions

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

phase-transitions-vaporization-and-condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Melting Points

Melting Points in Organic Chemistry
The melting point of a compound is the temperature at which the solid phase transitions into the liquid phase at a ...

Boiling Points

Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

Explain how physical and chemical properties of substances are related to their usage in everyday life such as in sunscreen, cookware, industrial applications, and fuels.

IPC.7.C

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

Metal Flame Emission

Metal Flame Emission
Flame testing is an analytical technique where a sample is placed in a flame, and the characteristic flame color is used to identify ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

Explain how electrons can transition from a high energy level to a low energy state, emitting photons at different frequencies for different energy transitions.

IPC.7.D

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

Balmer Series

The Bohr Model
Niels Bohr proposed a model for the hydrogen atom in 1913 that described discrete energy states are associated with a fixed electron orbit ...

Beer's Law

Absorbance and Fluorescence
When light hits a substance, it is either absorbed, transmitted, or reflected. Typically, a substance interacts with a range ...

The Wave Nature of Light

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms ...

Explain how atomic energy levels and emission spectra present evidence for the wave particle duality.

IPC.7.E

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Finding Rate Law from Initial Rates

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