**Quantized Energy**

__The Nature of Matter__ - In the early 1900's, * Max Planck* discovered that

__matter__cannot absorb or emit

*amount of energy.*

**any**Instead...

He postulated that energy can only be gained or lost in whole-number multiples of the quantity **h v**

➞ so, the change in energy (ΔE) is calculated by: **ΔE = nh v**

As you can see in the above image,

**h** ➞ Planck's constant = 6.626 x 10^{-34} J^{.}s* v* ➞ the frequency = Hz, or s

^{-1}

**n**➞ an integer = 1, 2, 3...

Because energy is transferred (absorbed or emitted) in these finite quantities, or "__packets of energy__," the energy is said to be ** quantized**.

- __quantized__ = only occurs in discrete units of size "hv"

-----

*ex:* What quantum of energy is emitted by CuCl at a wavelength of 450. nm?

- use the given wavelength (λ) to find the frequency (*v*)

- then find the "packet" or "quantum" of energy using ΔE = nh*v* (with n = 1)...

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**Photons, and the Wave-Particle Duality of Light**

__Einstein__ continued with Planck's research (above), and suggested that EMR ("light") can exhibit the same type of behavior as exhibited by __matter__ in Planck's above postulation.

Einstein proposed that EMR can be viewed as a __stream of "particles__" called ** photons**.

- __photons__ = a "packet" or "quantum" of light.

This proposal led to...

**The Wave-Particle Duality of Light**

➞ __wave-particle duality of light__ = a phenomenon in which light can exhibit both wave-like and particle-like behavior.

➞ the energy of a photon is given by: **E _{photon} = hv = hc / λ**

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**The de Broglie Wavelength**

After Einstein's wave-particle duality of * light*, scientists, including

__de Broglie__, began considering if

*could also act as either a wave or a particle...*

**matter**__Matter__, previously thought to behave (and travel through space) as a particle, can ** also** show wave-like characteristics as well.

➞ **de Broglie** = found a relationship between __mass__ and __wavelength__: **λ = h/mv**

Let's do an example...

*ex:* Compare the wavelength for an electron (mass = 9.11 x 10

^{-31}kg) traveling at a speed of 1.0 x 10

^{7}m/s with that for a ball (mass = 0.10 kg) traveling at 35 m/s. (1 J = 1 kg

^{.}m

^{2}/ s

^{2}).

-- we'll perform the calculations side by side, then compare...

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**Photoelectric Effect**

__Photoelectric Effect__ = the observation that many metals emit electrons when light shines upon them.

**Threshold Frequency**

The light used to dislodge the electrons must have a high enough energy such that it meets or exceeds the __threshold frequency__ (Φ).

➞ a single photon must have enough energy (h*v*) to dislodge an electron which is * bound* to the metal with a

__binding energy__= Φ

➞ so, the __threshold frequency__ condition is: **h v ≥ Φ**

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In my next post covering **SECTION 7 - Quantum-Mechanical View of the Atom, and Periodicity**,

We'll discuss the Atomic Spectrum of Hydrogen and the Bohr Model of the Atom.