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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Identify the relationship between energy and wavelength using the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J s} \), \( c \) is the speed of light \( 3.00 \times 10^8 \text{ m/s} \), and \( \lambda \) is the wavelength.

Rearrange the equation to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \).

Substitute the given energy threshold \( E = 7.22 \times 10^{-19} \text{ J} \) into the equation.

Substitute the values for Planck's constant \( h \) and the speed of light \( c \) into the equation.

Calculate the wavelength \( \lambda \) using the substituted values to find the wavelength of radiation that provides a photon of the given energy.

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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 or radiation of sufficient energy. This effect demonstrates the particle nature of light, as photons must have energy exceeding a certain threshold to dislodge electrons from the surface of a material, which is specific to each element.

Energy of a Photon

The energy of a photon is directly related to its frequency and inversely related to its wavelength, described by the equation E = hν = hc/λ, where E is energy, h is Planck's constant, ν is frequency, c is the speed of light, and λ is wavelength. This relationship is crucial for determining the wavelength of radiation needed to achieve a specific energy threshold.

Planck's Constant

Planck's constant (h) is a fundamental constant in quantum mechanics, valued at approximately 6.626 x 10^-34 J·s. It relates the energy of a photon to its frequency, serving as a bridge between the macroscopic and quantum worlds. Understanding this constant is essential for calculating the energy of photons in the context of the photoelectric effect.

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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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