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?

Verified step by step guidance

1. 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.
2. Rearrange the equation to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \).
3. Substitute the given energy threshold \( E = 7.22 \times 10^{-19} \text{ J} \) into the equation.
4. Substitute the values for Planck's constant \( h \) and the speed of light \( c \) into the equation.
5. Calculate the wavelength \( \lambda \) using the substituted values to find the wavelength of radiation that provides a photon of the given energy.

Key Concepts

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.