Which of the following metals will exhibit the photoelectric effect when illuminated with light of wavelength 400 nm?

• A. Copper (work function = 4.70 eV)
• B. Calcium (work function = 2.87 eV)
• C. Platinum (work function = 6.35 eV)
• D. Sodium (work function = 2.28 eV)

Answer: (D)

Verified step by step guidance

1. Understand that the photoelectric effect occurs when photons of light have enough energy to eject electrons from the surface of a metal. The minimum energy required to eject an electron is called the work function (\( \phi \)) of the metal.
2. Calculate the energy of the incident photons using the wavelength of the light. Use the formula for photon energy: \[ E = \frac{hc}{\lambda} \] where: - \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \)) - \( c \) is the speed of light (\(3.00 \times 10^{8} \, \text{m/s} \)) - \( \lambda \) is the wavelength of the light (400 nm, convert to meters: \(400 \times 10^{-9} \, \text{m} \))
3. Convert the photon energy from joules to electron volts (eV) using the conversion factor: \[ 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \]
4. Compare the photon energy (in eV) to the work function of each metal. If the photon energy is greater than or equal to the work function, the metal will exhibit the photoelectric effect under illumination with that wavelength.
5. Identify which metals have work functions less than or equal to the photon energy calculated. These metals will emit electrons when illuminated with 400 nm light.