Wave Properties and Photon Energy

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Questions and Answers

What is the amplitude in the wave diagram?

  • A
  • C (correct)
  • D
  • B

Wavelength and frequency are directly proportional to each other.

False (B)

What is the frequency of a photon with a wavelength of 546 nm?

5.44 × 10^14 Hz

The energy of a photon is given by the formula E = hν, where h is ___ constant.

<p>Planck's</p> Signup and view all the answers

Match the following properties to their corresponding symbols:

<p>Frequency = ν Wavelength = λ Energy = E Amplitude = A</p> Signup and view all the answers

If the wavelength of a photon is 8.73 cm, what is its energy in joules?

<p>22.22 × 10^-2 J (B)</p> Signup and view all the answers

There are 6.022 × 10^23 photons in one mole.

<p>True (A)</p> Signup and view all the answers

Calculate the frequency (in Hz) of one photon from 2 moles with a total energy of 1.13 J.

<p>9.38 × 10^-25 Hz</p> Signup and view all the answers

The conservation of energy requires that the energy of a single photon equals ___ times the number of photons.

<p>total energy</p> Signup and view all the answers

Which early 20th century phenomenon specifically demonstrated light’s particle properties?

<p>The photoelectric effect (C)</p> Signup and view all the answers

In the Bohr model of the atom, electrons absorb energy when moving to orbits with a larger radius.

<p>True (A)</p> Signup and view all the answers

What happens to the energy levels of an electron in the Bohr model as the principal quantum number n increases?

<p>The spacing of energy levels increases.</p> Signup and view all the answers

The formula to calculate the frequency of light absorbed during an electron transition is ______.

<p>E = hν</p> Signup and view all the answers

Match each electron transition to its corresponding line in the atomic emission spectrum:

<p>n = 1 to n = 2 = D n = 1 to n = 3 = C n = 1 to n = 4 = B n = 1 to n = 5 = A n = 3 to n = 4 = F n = 2 to n = 3 = E</p> Signup and view all the answers

What is the frequency (Hz) of light absorbed when an electron in a hydrogen atom transitions from n = 2 to n = 5?

<p>6.999999 × 10^11 Hz (C)</p> Signup and view all the answers

All objects possess ______ wavelengths that illustrate their wave-particle duality.

<p>de Broglie</p> Signup and view all the answers

De Broglie wavelengths are significant for everyday objects like baseballs.

<p>False (B)</p> Signup and view all the answers

What is the formula used to calculate the energy of a photon?

<p>E = hc/λ (A), E = hν (D)</p> Signup and view all the answers

Photons have mass.

<p>False (B)</p> Signup and view all the answers

What is the momentum of a photon with a wavelength of 638 nm?

<p>1.00 × 10^-22 kg·m/s</p> Signup and view all the answers

The energy of a photon emitted from an electron falling from n=3 to n=1 in a hydrogen atom is _______ J.

<p>-1.937 × 10^-18</p> Signup and view all the answers

Match the following concepts with their respective values or descriptions:

<p>Wavelength of photon = 638 nm Planck's constant (h) = 6.626 × 10−34 J·s Speed of light (c) = 3 × 10^8 m/s Energy transition for hydrogen = −1.937 × 10−18 J</p> Signup and view all the answers

How is the energy of 6.75 moles of photons with a wavelength of 612 nm expressed in kJ?

<p>4.23 kJ (D)</p> Signup and view all the answers

The momentum of a photon can be expressed as p = λh.

<p>False (B)</p> Signup and view all the answers

What is the energy change (∆E) for the transition of an electron in hydrogen falling from n=3 to n=1?

<p>-1.937 × 10^-18 J</p> Signup and view all the answers

Planck's constant can be expressed as _______ J·s.

<p>6.626 × 10−34</p> Signup and view all the answers

Which of the following values represents the speed of light?

<p>3.00 × 10^8 m/s (D)</p> Signup and view all the answers

Flashcards

Amplitude

The maximum displacement of a wave from its equilibrium position.

Wavelength

The distance between two corresponding points on a wave, such as two consecutive crests or troughs.

Frequency

The number of wave cycles that pass a given point per unit of time.

Photon Wavelength (visible light)

The wavelength of a photon of visible light is 546 nm.

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Photon Frequency (GHz)

Calculated by c = νλ. (Result 5.44x 10^14 Hz).

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Microwave Photon Wavelength

A microwave photon has a wavelength of 8.73 cm.

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Microwave Photon Energy

Calculated by E = hc/λ. (Result: 2.22x 10^-22 J).

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Photon Energy (from moles)

Energy of two moles of photons is 1.13 J. The calculation required finding the energy per photon in which the result was 9.38x 10^-25J

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Photon Frequency (from Energy)

Calculated by finding the frequency of one photon. (Result: 1.41x 10^19 Hz).

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Units of Energy

Energy is measured in Joules (J).

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Photoelectric effect

Light's particle nature was demonstrated by the observation that light can eject electrons from a material.

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Bohr model of the atom

Electrons orbit the nucleus in specific energy levels/shells.

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Electrons energy levels

Electron transitions between energy levels emit or absorb specific frequencies of light.

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Energy level transition frequency calculation

The frequency of absorbed light during a transition can be calculated using the difference in energy levels and Planck's constant.

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Atomic emission spectrum

A set of specific frequencies (or wavelengths) of light emitted by an atom when its electrons transition between energy levels.

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Electron transition

Movement of an electron from one energy level to another.

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De Broglie wavelength

Every particle has an associated wave nature, wavelength of particles.

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De Broglie wavelength calculation

The de Broglie wavelength of a particle is related to its momentum and Planck's constant.

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Photon Momentum

The momentum of a photon is calculated using the equation: p = h/λ, where h is Planck's constant and λ is the wavelength of the photon.

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Electron Energy Transition

When an electron in a hydrogen atom transitions from a higher energy level (n=3) to a lower energy level (n=1), it emits a photon with energy equal to the difference in energy between the two levels.

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Photon Energy

The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This relationship is described by the equation E = hν = hc/λ.

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Energy of Multiple Photons

The total energy of a group of photons can be calculated by multiplying the energy of a single photon by the number of photons.

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Photon Energy (kJ/mol)

The energy of a mole of photons can be calculated using the following equation: E = (hc/λ) * N, where N is Avogadro's number.

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What is the momentum of a photon?

The momentum of a photon is defined as p = h/λ, where h is Planck's constant and λ is its wavelength.

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What happens to an electron when it changes energy levels?

When an electron in a hydrogen atom transitions from a higher energy level to a lower energy level, it emits a photon with an energy equal to the difference in energy between the two levels.

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How is the energy of a photon related to its frequency and wavelength?

Photon energy is directly proportional to its frequency and inversely proportional to its wavelength, which is described by the equation E = hν = hc/λ.

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How is the energy of multiple photons calculated?

To calculate the total energy of a group of photons, multiply the energy of a single photon by the number of photons.

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How do you calculate the energy of a mole of photons?

The energy of a mole of photons can be calculated using the equation: E = (hc/λ) * N, where N is Avogadro's number.

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Study Notes

Wave Properties

  • Amplitude: The maximum displacement of a wave from its equilibrium position. Corresponds to the height of a wave.
  • Wavelength: The distance between two consecutive corresponding points of a wave, such as two crests or two troughs.
  • Frequency: The number of waves that pass a given point in a unit of time. Often measured in Hertz (Hz).

Photon Energy

  • Wavelength and Frequency (Visible Light): The wavelength of 546 nm wavelength of light translates to a frequency of 5.49 x 105 GHz. This calculation uses the speed of light (c) and the fundamental equation: c = νλ

  • Photon Energy Calculation: The energy of a photon is calculated using the equation E = hc/λ; where h is Planck's constant, c is the speed of light, and λ is the wavelength.

  • Energy and Frequency (Microwaves): A microwave photon with a wavelength of 8.73 cm has an energy of 2.28 x 10-24 Joules.

  • Moles of Photons and Energy: 2 moles of photons with a total energy of 1.13 Joules have a frequency of 1.42 x 1015 Hz for each photon.

Atomic Structure and Light

  • Bohr Model: Electrons absorb energy and move to higher energy levels (orbits), increasing in n values. The model predicts that the spacing between energy levels changes with increasing n values.

  • Electron Transitions and Frequency: The frequency of light absorbed when an electron transitions from n=2 to n=5 in a hydrogen atom is 6.906 x 1014 Hz. This calculation uses the equation ΔE = hν and the appropriate energy change.

  • Atomic Emission Spectra: A spectrum displaying the wavelengths of light emitted by an atom with the possible transitions for emitted lines labeled.

  • Atomic Emission Transitions: Transitions are expressed as ninitial → nfinal (example: n=1 to n=2). Each transition corresponds with a characteristic emitted wavelength.

  • Electron Closest to Zero Energy: At the end of particular transitions in a diagram illustrating atomic transitions, the electron is closest to zero energy.

Wave-Particle Duality and Momentum

  • De Broglie Wavelength The De Broglie wavelength is calculated using the equation λ = h/p, where h is Planck's constant, and p is momentum.

  • De Broglie Wavelength Example: A 144 grame baseball thrown at 95.3 mph has a de Broglie wavelength of 1.08 x 10-34 m

  • Momentum of a Photon Calculation: The momentum of a photon with a wavelength of 638 nm is 1.04 x 10-27 kg·m/s. This utilizes the equation p = h/λ.

Energy of Photons

  • Energy in Electron Transitions: An electron transitioning from n=3 to n=1 in a hydrogen atom releases photon energy of approximately 1.94 x 10-18 Joules.

  • Energy of Multiple Photons (Example): 6.75 moles of photons, with each photon having a wavelength of 612 nm has an energy of 1.32 x 103 kJ. The equation E = hc/λ is used.

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