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Waves & Bohr’s Theory Chapter 7 §1-4

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**Waves Wavelength, λ, in meters (m)**

The length of a wave from crest to crest or trough to trough. Frequency, υ, in inverse seconds (s-1) The number of waves that pass in a given amount of time.

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**Light’s Wave Characteristics**

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**Light’s Wave Characteristics**

Speed of light equation c = speed of light, 3.00x108 m/s λ = wavelength, in m ν = frequency, in Hz or s–1

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**Light’s Wave Characteristics**

What is the frequency of red light having a wavelength of 681 nm? 681 nm = 6.81x10–7 m 3.0x108 m/s = (6.81x10–7 m)(υ) υ = 4.41x1014 s–1

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Max Planck Quantized

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Planck’s Equation n = integer other than zero, no unit, represents the energy level of the atom h = Planck’s constant, 6.63x10–34 J•s ν = frequency, in Hz or s–1 E = energy of a quantum – amount of energy to move an e– from its present energy to its next higher one

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**The Photoelectric Effect**

Although the photoelectric effect was first discovered by Heinrich Hertz in 1887, Albert Einstein incorporated Planck’s ideas into the explanation of the photoelectric effect.

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**The Photoelectric Effect**

Einstein stated that electrons could move within their atoms if a minimum amount of energy were reached.

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Let’s Practice The blue-green line of the hydrogen atom spectrum has a wavelength of 486 nm. What is the energy of a photon of this light? 486 nm = 4.86x10–7 m 3.0x108 m/s = (4.86x10–7 m) (υ) υ = 6.17x1014 s–1 E = (1)(6.63x10–34 J•s)(6.17x1014 s–1) E = 4.09x10–19 J

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Bohr’s Line Spectra Bohr noticed that elements emitted a line spectrum.

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Bohr’s Line Spectra He hypothesized that each line in the spectra were created when an electron fell from a higher energy level to a lower one within the atom.

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Bohr’s Line Spectra Here, the electron of the hydrogen atom is shown moving between the various energy levels.

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**Bohr’s Postulates Bohr felt the need to explain two main issues:**

1st – If electrons are negative and protons are positive…..

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**Bohr’s Postulates Bohr felt the need to explain two main issues:**

2nd – How are the line spectra being created?

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**Bohr’s Postulates Postulate #1:**

Electrons only have specific energy values and energy levels. = the energy of a particular e– energy level = the Rydberg constant = 2.18x10–18 J = integral value representing the energy level (principal quantum number

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**Bohr’s Postulates Postulate #2:**

Electrons become excited by collisions of atoms or absorption of energy – think of anything colored… it absorbs light to later emit (reflect) other colors Electrons can change energy only by going from one energy level to another – making a transition.

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Bohr’s Postulates Postulate #2: The electron absorbing energy

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**Bohr’s Postulates Postulate #2:**

When an electron falls from a higher energy level to a lower energy level, it emits a photon of light.

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**Bohr’s Postulates Postulate #2:**

This energy of this photon can be found by:

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**Bohr’s Postulates Postulate #2:**

Remember that the energy of a photon can be determined by:

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Bohr’s Postulates Postulate #2: Which can be related to wavelength:

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**Bohr’s Postulates Postulate #2: Which leads to the Balmer equation:**

This equation can calculate the wavelength of any electron falling to the 2nd energy level – emitting visible light.

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**Bohr’s Postulates Postulate #2:**

By the end of Experiment #13, you should be able to identify the Balmer Series, along with the Paschen Series and the Lyman Series.

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Let’s Practice What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from energy level n = 6 to level n = 3?

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Let’s Practice What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from energy level n = 6 to level n = 3? ∆E = E3 – E6 = υ = 2.74x1014 s–1 c = λυ → 3.0x108 m/s = λ (2.74x1014 s–1) λ = 1.09x10–6 m = 1090 nm (Infrared)

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