9. Quantum Mechanics

The Energy of Light

What Is Light?

The concentration of H2O in the stratosphere is about 5 ppm. It undergoes photodissociation according to: H2O1g2 ¡ H1g2 + OH1g2 (b) Using Table 8.3, calculate the wavelength required to cause this dissociation.

If human height were quantized in 1-cm increments, what
would happen to the height of a child as she grows up:
(i) the child’s height would never change, (ii) the child’s
height would continuously increase, (iii) the child’s height
would increase in jumps of 6 cm, or (iv) the child’s height
would increase in “jumps” of 1 cm at a time?

(b) Use the energy requirements of these two pro- cesses to explain why photodissociation of oxygen is more important than photoionization of oxygen at altitudes below about 90 km.

A 5.00-mL ampule of a 0.100-M solution of naphthalene in hexane
is excited with a flash of light. The naphthalene emits 15.5 J
of energy at an average wavelength of 349 nm. What percentage
of the naphthalene molecules emitted a photon?

A laser produces 20.0 mW of red light. In 1.00 hr, the laser emits
2.29 * 1020 photons. What is the wavelength of the laser?

(a) Calculate the energy of a photon of electromagnetic
radiation whose frequency is 2.94 * 1014 s - 1.

Calculate the energy (in nJ) of a photon emitted by a mercury lamp with a frequency of 6.88 x 1014 Hz.

(b) Calculate 
the energy of a photon of radiation whose wavelength is 413 
nm.

A light ray has a wavelength that is 835 µm contains 6.32 x 10-3 J of energy. How many photons does this light ray have?

Ionization involves completely removing an electron from an atom.
How much energy is required to ionize a hydrogen atom in its
ground (or lowest energy) state? What wavelength of light contains
enough energy in a single photon to ionize a hydrogen atom?

What is the energy (in kJ) of one mole of photons of ultraviolet light with a wavelength of 85 nm? (LO 5.3)
(a) 1.4 * 10-6 kJ
(b) 1.4 * 103 kJ
(c) 2.4 * 1014 kJ
(d) 2.4 * 10-15 kJ

A laser pulse with wavelength 532 nm contains 3.85 mJ of
energy. How many photons are in the laser pulse?

Red light with a wavelength of 660 nm from a 3.0 mW diode 
laser shines on a solar cell. 
(b) How much current (in amperes) flows in the circuit of 
the solar cell if all the photons are absorbed by the cell 
and each photon produces one electron?

The Energy of Light Example 1

The watt is the derived SI unit of power, the measure of
energy per unit time: 1 W = 1 J>s. A semiconductor laser in
a DVD player has an output wavelength of 650 nm and a
power level of 5.0 mW. How many photons strike the DVD
surface during the playing of a DVD 90 minutes in length?

Light: Crash Course Astronomy #24

What the HECK is a Photon?!

The human eye contains a molecule called 11-cis-retinal that
changes shape when struck with light of sufficient energy. The
change in shape triggers a series of events that results in an electrical
signal being sent to the brain that results in vision. The
minimum energy required to change the conformation of
11-cis-retinal within the eye is about 164 kJ>mol. Calculate the
longest wavelength visible to the human eye.

A heat lamp produces 32.8 watts of power at a wavelength of
6.5 mm. How many photons are emitted per second?
(1 watt = 1 J/s)

Calculate the energy of a photon of electromagnetic radiation at
each of the wavelengths indicated in Problem 39.
a. 632.8 nm (wavelength of red light from helium–neon laser)
b. 503 nm (wavelength of maximum solar radiation)
c. 0.052 nm (wavelength contained in medical X-rays)

One type of sunburn occurs on exposure to UV light of
wavelength in the vicinity of 325 nm. (d) These UV
photons can break chemical bonds in your skin to cause
sunburn—a form of radiation damage. If the 325-nm radiation
provides exactly the energy to break an average chemical
bond in the skin, estimate the average energy of these
bonds in kJ>mol.

According to the equation for the Balmer line spectrum of hydrogen, a value of n = 3 gives a red spectral line at 656.3 nm, a value of n = 4 gives a green line at 486.1 nm, and a value of n = 5 gives a blue line at 434.0 nm. Calculate the energy in kilojoules per mole of the radiation corresponding to each of these spectral lines.

Light Energy

The rate of solar energy striking Earth averages 168 watts per square meter. The rate of energy radiated from Earth’s surface averages 390 watts per square meter. Comparing these numbers, one might expect that the planet would cool quickly, yet it does not. Why not?

What is Light? Maxwell and the Electromagnetic Spectrum

Calculate the energies of the following waves in kilojoules per mole, and tell which member of each pair has the higher value.
(a) An FM radio wave at 99.5 MHz and an AM radio wave at 1150 kHz

What is the energy of each of the following photons in kilojoules per mole?
(a) v = 5.97 * 1019 s-1
(b) v = 1.26 * 106 s-1 
(c) <lamba> = 2.57 * 102 m

Alcohol-based fuels for automobiles lead to the production of formaldehyde (CH2O) in exhaust gases. Formaldehyde undergoes photodissociation, which contributes to photo- chemical smog: CH2O + hn ¡ CHO + H The maximum wavelength of light that can cause this reac- tion is 335 nm. (b) What is the maximum strength of a bond, in kJ>mol, that can be bro- ken by absorption of a photon of 335-nm light?

Which wave corresponds to higher energy radiation? (LO 5.1)
(a) <img src="" alt="" />
(b) <img src="" alt="" />

Determine the energy of 1 mol of photons for each kind of light.
(Assume three significant figures.)
a. infrared radiation (1500 nm)

The Energy of Light Example 2

How much energy (in kJ) do 4.50 moles of photons contain at a wavelength of 705 nm?

An AM radio station broadcasts at 1000 kHz and its FM
partner broadcasts at 100 MHz. Calculate and compare the
energy of the photons emitted by these two radio stations.

The dissociation energy of a carbon-bromine bond is typically about 276 kJ/mol. (a) What is the maximum wavelength of photons that can cause C-Br bond dissociation?

Where does the energy come from to evaporate the esti- mated 425,000 km3 of water that annually leaves the oceans, as illustrated here? [Section 18.3]

One watt (W) is equal to 1 J/s. Assuming that 5.0% of the energy output of a 75 W light bulb is visible light and that the average wavelength of the light is 550 nm, how many photons are emitted by the light bulb each second?

Iron is commonly found as Fe, Fe2+, and Fe3+.
(c) The third ionization energy of Fe is Ei3 = +2952 kJ/mol. What is the longest wavelength of light that could ionize Fe2+1g2 to Fe3+1g2?

One type of sunburn occurs on exposure to UV light of 
wavelength in the vicinity of 325 nm. (c) How many photons 
are in a 1.00 mJ burst of this radiation?

A photovoltaic cell contains a p–n junction that that converts 
solar light to electricity. An optimum semiconductor 
would have its band-gap energy matched to the wavelength 
of maximum solar intensity at the Earth’s surface. 
(b) Which of the following semiconductors absorb at a 
wavelength matched with maximum solar intensity? 
CdTe with a band-gap energy of 145 kJ/mol or ZnSe 
with a band-gap energy of 248 kJ/mol.

Why Does Light REALLY Bend?

How much energy is contained in 1 mol of each?
a. X-ray photons with a wavelength of 0.135 nm
b. g-ray photons with a wavelength of 2.15 * 10-5 nm

If a sample of calcium chloride is introduced into a nonluminous 
flame, the color of the flame turns to orange 
(“flame test”). The light is emitted because calcium atoms 
become excited; their return to the ground state results in 
light emission. (b) What is the energy of 
1.00 mol of these photons (a mole of photons is called an 
Einstein)?

Microwave ovens work by irradiating food with microwave radiation, which is absorbed and converted into heat. Assum-ing that radiation with l = 15.0 cm is used, that all the energy is converted to heat, and that 4.184 J is needed to raise the temperature of 1.00 g of water by 1.00 °C, how many photons are necessary to raise the temperature of a 350 mL cup of water from 20 °C to 95 °C?

Ultraviolet radiation and radiation of shorter wavelengths can
damage biological molecules because these kinds of radiation
carry enough energy to break bonds within the molecules. A
typical carbon–carbon bond requires 348 kJ>mol to break.
What is the longest wavelength of radiation with enough energy
to break carbon–carbon bonds?

(b) What is the energy of one of these photons?

Calculate the energy of a photon of electromagnetic radiation at
each of the frequencies indicated in Problem 40.
a. 100.2 MHz (typical frequency for FM radio broadcasting) 
b. 1070 kHz (typical frequency for AM radio broadcasting) 
(assume four significant figures) 
c. 835.6 MHz (common frequency used for cell phone 
communication)

Consider the electronic structure of the element bismuth.
(a) The first ionization energy of bismuth is Ei1 = +703 kJ/ mol. What is the longest possible wavelength of light that could ionize an atom of bismuth?

A particular laser consumes 150.0 watts of electrical power and
produces a stream of 1.33 * 1019 1064-nm photons per second.
What is the percent efficiency of the laser in converting electrical
power to light?

Why Doesn't Light Have Mass?

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Professor Dave Explains

1. Intro to General Chemistry

2. Atoms & Elements

3. Chemical Reactions

4. BONUS: Lab Techniques and Procedures

5. BONUS: Mathematical Operations and Functions

6. Chemical Quantities & Aqueous Reactions

7. Gases

8. Thermochemistry

10. Periodic Properties of the Elements

11. Bonding & Molecular Structure

12. Molecular Shapes & Valence Bond Theory

13. Liquids, Solids & Intermolecular Forces

14. Solutions

15. Chemical Kinetics

16. Chemical Equilibrium

17. Acid and Base Equilibrium

18. Aqueous Equilibrium

19. Chemical Thermodynamics

20. Electrochemistry

21. Nuclear Chemistry

22. Organic Chemistry

23. Chemistry of the Nonmetals

24. Transition Metals and Coordination Compounds

[BOOK CHEM] Clutch Version

Wavelength and Frequency

Wavelength&nbsp;is the distance from one crest of a wave to another, whereas frequency is the number of waves within a second.&nbsp;

Quantum Numbers: Spin Quantum Number

The Spin Quantum Number deals with the spin of an electron within an orbital.

Speed of Light

The Speed of Light in a vacuum is related to the wavelength and frequency of a light particle.

Bohr Equation

In the Bohr Equation, the energy and wavelength a photon is related to its energy shell transitions.

Quantum Numbers: Angular Momentum Quantum Number

The&nbsp;Angular Momentum Quantum Number&nbsp;gives the shape of the atomic orbitals.

Emission Spectrum

Emission Spectra is a series of lines formed when emitted light is focused by a slit and passed through a prism. &nbsp;

Introduction to Quantum Mechanics

The 4 Quantum Numbers provide us the coordinates to find the theoretical location of an electron.

Quantum Numbers: Nodes

A node is the region in an atom with zero electron density and where an electron is least likely to exist.

The Energy of Light&nbsp;involves the use of a new variable Planck's Constant.

Electromagnetic Spectrum

The Electromagnetic Spectrum is the different forms of radioactive energy that exists in our universe.

Heisenberg Uncertainty Principle

Heisenberg's Uncertainty Principle&nbsp;tries to explain the potential duality of an electron behaving as either a particle or wave.&nbsp;

Quantum Numbers: Number of Electrons

The Quantum Numbers can give both the quantity and location of electrons within a given atom.&nbsp;

Quantum Numbers: Principal Quantum Number

The Principal Quantum Number gives both the size and energy of an electron shell.&nbsp;

Photoelectric Effect

What happens when light strikes the surface of a metal? The Photoelectric Effect&nbsp;can help to explain that.&nbsp;

Quantum Numbers: Magnetic Quantum Number

The Magnetic Quantum Number gives the location of an electron within a specific orbital.

Bohr Model

In the Bohr Model, electrons can move up and down to different orbitals or shells based on absorbing or releasing of energy.&nbsp;

De Broglie Wavelength

The&nbsp;De Broglie Wavelength equation relates wavelength to velocity or speed.&nbsp;