ChemistNate
  • Home / Ask Me Stuff
  • Lessons
    • Thermodynamics >
      • Thermochemistry Worksheet + Answers
      • First Law of Thermodynamics
      • Pressure-Volume Work
      • Enthalpy
      • Hess' Law
      • Enthalpy of Formation
      • Heat Capacity
      • Calorimetry
      • Entropy
      • Third Law of Thermodynamics
      • Spontaneity: Gibbs Free Energy
      • Second Law of Thermodynamics
      • Spontaneity at Different Temperatures
    • Electrochemistry >
      • Redox Reactions
      • Introduction to Half-Reactions
      • Calculating Oxidation Number
      • Has a Redox Reaction Occurred?
      • How to Balance Redox Reactions (Acidic Solution)
      • How to Balance Redox Reactions (Basic Solution)
      • Galvanic Cells
      • Standard Reduction Potentials
      • Electrolytic Cells
      • Nernst Equation
    • Kinetics >
      • Introduction
      • Relative Rates of Reaction
      • Rate Laws
      • Zero-Order Reactions
      • First-Order Reactions
      • Second-Order Reactions
      • Half-Life Expressions
      • Arrhenius Equation
      • How Long will it Take to Decay?
      • What Order is this Reaction?
      • Find the Rate Constant
      • Find the Activation Energy
    • Gases >
      • Pressure, Volume, Temperature
      • Ideal Gas Law
      • Density of Gases
      • Ideal Gas Law and Changes in P, V, T
      • Kinetic Molecular Theory
      • van der Waals' Equation for Non-Ideal Gases
      • Partial Pressures
      • Kinetic Energy and Temperature
    • Equilibrium >
      • Writing Equilibrium Expressions
      • Le Chatelier's Principle
    • Acids and Bases >
      • Acids and Bases Worksheet + Answers
      • Arrhenius vs Bronsted-Lowry vs Lewis Acids
      • Solve Titration Questions
    • Intermolecular Forces >
      • Phase Diagrams
      • Phase Changes
      • Intermolecular Forces
      • Effects of Intermolecular Forces
      • Ranking by Boiling/Melting Point
      • Clausius-Clapeyron Equation
      • Heating Curves
    • Solids >
      • Ionic/Metallic/Covalent
      • Symmetry of Solids
      • Simple Cubic, fcc and bcc
      • How to Find Edge Length
    • Organic Reactions >
      • Br2 + Alkene (Adding across a double bond)
      • HCl + Alkene (Adding across a double bond)
      • Reaction of OH with Alkyl Halide
      • What is Regioselectivity?
    • Moles and Mass >
      • Average Atomic Mass
      • Solve for Isotopic Abundance
      • Limiting Reagents
      • Percent Yield
      • Actual Yield and Percentage Yield
      • Percent Composition
    • Atomic Structure >
      • What's in an Atom?
      • Quantum Numbers
      • Pauli, Aufbau, Hund
      • Light: E h ν λ
      • Energy Levels of Hydrogen
      • Energy Levels of Non-Hydrogen Atoms
    • Organic Naming >
      • Naming Organic Molecules
      • How to Name Amines
      • How to Name Amides
  • Privacy Policy
  • Lewis Structures
  • Home / Ask Me Stuff
  • Lessons
    • Thermodynamics >
      • Thermochemistry Worksheet + Answers
      • First Law of Thermodynamics
      • Pressure-Volume Work
      • Enthalpy
      • Hess' Law
      • Enthalpy of Formation
      • Heat Capacity
      • Calorimetry
      • Entropy
      • Third Law of Thermodynamics
      • Spontaneity: Gibbs Free Energy
      • Second Law of Thermodynamics
      • Spontaneity at Different Temperatures
    • Electrochemistry >
      • Redox Reactions
      • Introduction to Half-Reactions
      • Calculating Oxidation Number
      • Has a Redox Reaction Occurred?
      • How to Balance Redox Reactions (Acidic Solution)
      • How to Balance Redox Reactions (Basic Solution)
      • Galvanic Cells
      • Standard Reduction Potentials
      • Electrolytic Cells
      • Nernst Equation
    • Kinetics >
      • Introduction
      • Relative Rates of Reaction
      • Rate Laws
      • Zero-Order Reactions
      • First-Order Reactions
      • Second-Order Reactions
      • Half-Life Expressions
      • Arrhenius Equation
      • How Long will it Take to Decay?
      • What Order is this Reaction?
      • Find the Rate Constant
      • Find the Activation Energy
    • Gases >
      • Pressure, Volume, Temperature
      • Ideal Gas Law
      • Density of Gases
      • Ideal Gas Law and Changes in P, V, T
      • Kinetic Molecular Theory
      • van der Waals' Equation for Non-Ideal Gases
      • Partial Pressures
      • Kinetic Energy and Temperature
    • Equilibrium >
      • Writing Equilibrium Expressions
      • Le Chatelier's Principle
    • Acids and Bases >
      • Acids and Bases Worksheet + Answers
      • Arrhenius vs Bronsted-Lowry vs Lewis Acids
      • Solve Titration Questions
    • Intermolecular Forces >
      • Phase Diagrams
      • Phase Changes
      • Intermolecular Forces
      • Effects of Intermolecular Forces
      • Ranking by Boiling/Melting Point
      • Clausius-Clapeyron Equation
      • Heating Curves
    • Solids >
      • Ionic/Metallic/Covalent
      • Symmetry of Solids
      • Simple Cubic, fcc and bcc
      • How to Find Edge Length
    • Organic Reactions >
      • Br2 + Alkene (Adding across a double bond)
      • HCl + Alkene (Adding across a double bond)
      • Reaction of OH with Alkyl Halide
      • What is Regioselectivity?
    • Moles and Mass >
      • Average Atomic Mass
      • Solve for Isotopic Abundance
      • Limiting Reagents
      • Percent Yield
      • Actual Yield and Percentage Yield
      • Percent Composition
    • Atomic Structure >
      • What's in an Atom?
      • Quantum Numbers
      • Pauli, Aufbau, Hund
      • Light: E h ν λ
      • Energy Levels of Hydrogen
      • Energy Levels of Non-Hydrogen Atoms
    • Organic Naming >
      • Naming Organic Molecules
      • How to Name Amines
      • How to Name Amides
  • Privacy Policy
  • Lewis Structures

Energy Levels of Hydrogen


There's an easy way to think about electron energy, and there's a hard (but more mathematically correct) way.  Let's do this the easy way.

Each electron in an atom has a certain amount of energy.  Shells closer to the nucleus have the lowest energies ... that means n=1 has the lowest energy, and higher n means higher energy.  There is a limit though, and eventually if an electron gains enough energy, it will exit the atom altogether.

Hydrogen - the simplest atom

Hydrogen is the easiest atom to predict electron energy for, because it only has one electron.  Suppose an electron is excited from n=1 (on the left) to n=3 (on the right):
Picture
Picture
Picture
Q: How much energy did the electron have to gain to move like this?  What wavelength of light could cause this to happen?

A: For hydrogen, we have two formulas we can use ... one for energy, and one for wavelength:
Picture
Picture
where R is Rydberg's constant (1.097 x 10^-7 m^-1), ni is the INITIAL shell number and nf is the FINAL shell number.  h is still Planck's constant (6.626 x 10^-34 Js) and c is still the speed of light (3.0 x 10^8 m/s).

And so we can calculate wavelength OR energy of the photon from it too:
Picture
Picture
And so for this electron transition to occur, we need a photon with at least 1.938 x 10^-18 J ... which means its wavelength has to be 102.6 nm or shorter. The answers here are NEGATIVE because the photon is being ABSORBED by the electron...the photon is losing energy (the electron is gaining energy).

Sample Question

Q: How much energy is RELEASED when an electron falls from n=6 to n=2 in a hydrogen atom?  What wavelength is a photon with that amount of energy?

A: E = 7.572 x 10^-20 J.
wavelength = 2.63 x 10^-6 m = 2630 nm
Created by Nathan Oldridge (aka ChemistNATE).  All lessons here are Public Domain.