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Ch.6 - Electronic Structure of Atoms
Chapter 6, Problem 33c

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (c) If molybdenum is irradiated with light of wavelength of 240 nm, what is the maximum possible velocity of the emitted electrons?

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Convert the wavelength of the light from nanometers to meters by using the conversion factor: 1 nm = 1 x 10^{-9} m.
Calculate the energy of the photons using the equation E = \frac{hc}{\lambda}, where h is Planck's constant (6.626 x 10^{-34} J\cdot s), c is the speed of light (3.00 x 10^8 m/s), and \lambda is the wavelength in meters.
Determine the kinetic energy of the emitted electrons by subtracting the energy threshold from the photon energy: KE = E_{photon} - E_{threshold}.
Use the kinetic energy to find the maximum velocity of the emitted electrons with the equation KE = \frac{1}{2}mv^2, where m is the mass of an electron (9.11 x 10^{-31} kg).
Solve for the velocity v by rearranging the equation to v = \sqrt{\frac{2 \times KE}{m}}.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, as photons must have energy greater than a material's work function to eject electrons. 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 of the light.
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Photoelectric Effect

Energy of a Photon

The energy of a photon is directly related to its wavelength and can be calculated using the formula E = hc/λ. In this equation, h represents Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. For the photoelectric effect to occur, the energy of the incoming photon must exceed the material's energy threshold, or work function.
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Photon Energy Formulas

Kinetic Energy of Emitted Electrons

When a photon with energy greater than the work function of a material ejects an electron, the excess energy is converted into the kinetic energy of the emitted electron. The kinetic energy (KE) can be calculated using the equation KE = E - φ, where E is the energy of the incoming photon and φ is the work function. This relationship allows us to determine the maximum velocity of the emitted electrons using the kinetic energy formula KE = 1/2 mv², where m is the mass of the electron.
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Related Practice
Textbook Question

A stellar object is emitting radiation at 3.0 mm. (a) What type of electromagnetic spectrum is this radiation (b) If a detector is capturing 3.0 3 108 photons per second at this wavelength, what is the total energy of the photons detected in 1 day?

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Textbook Question

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (a) What is the frequency threshold for emission of electrons?

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Textbook Question

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (b) What wavelength of radiation will provide a photon of this energy?

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Open Question
Titanium metal requires light with a maximum wavelength of 286 nm to emit electrons. (a) What is the minimum energy of the photons necessary to emit electrons from titanium via the photoelectric effect? (b) If titanium is irradiated with light of wavelength 276 nm, what is the maximum possible kinetic energy of the emitted electrons?
Textbook Question

Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?

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Textbook Question

Classify each of the following statements as either true or false: (a) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths (b) a hydrogen atom in the n = 2 state is at a lower energy than one in the n = 1 state (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.

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