Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s - 1 before it can eject an electron from its surface via the photoelectric effect. (a) What is the minimum energy needed to eject an electron?

Verified step by step guidance

1. Identify the relationship between energy and frequency using the equation: \( E = h \nu \), where \( E \) is the energy, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \text{ J s} \)), and \( \nu \) is the frequency.
2. Substitute the given frequency \( \nu = 1.09 \times 10^{15} \text{ s}^{-1} \) into the equation.
3. Calculate the energy \( E \) by multiplying Planck's constant \( h \) with the frequency \( \nu \).
4. Ensure the units are consistent, with energy in joules (J).
5. Interpret the result as the minimum energy required to eject an electron from the surface of molybdenum.

Key Concepts

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light or electromagnetic radiation. This effect demonstrates the particle nature of light, as photons must have sufficient energy to overcome the work function of the material to eject electrons. The minimum frequency of radiation required to cause this emission is directly related to the energy of the incoming photons.

Energy-Frequency Relationship

The energy of a photon is directly proportional to its frequency, described by the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency of the radiation. This relationship allows us to calculate the energy associated with a specific frequency of light, which is crucial for determining the minimum energy needed to eject an electron in the photoelectric effect.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It has a value of approximately 6.626 x 10^-34 J·s. Understanding this constant is essential for calculations involving the energy of photons, particularly in the context of the photoelectric effect, where it helps determine the energy required to eject electrons from a material.