Question

the work functions for sodium, cesium, copper, and iron are 2.3, 2.1, 4.7, and 4.5ev, respectively. when red light of 400nm shines on each of these metals, which would emit electrons? for those that emit electrons, give the electrons' maximum kinetic energy.

Answer 1

Red light of 400 nm wavelength will cause the emission of electrons from sodium and cesium metals since their work functions are less than the photon energy. The emitted electrons will have a maximum kinetic energy of 0.8 eV for sodium and 1.0 eV for cesium.

Step-by-step explanation:

The question relates to the photoelectric effect, which is a phenomenon in physics where electrons are emitted from materials, typically metals, when they absorb energy from light. The amount of energy required to emit an electron from the surface of a metal is known as the work function of the material.

Red light of 400 nm wavelength corresponds to an energy of approximately 3.1 eV (using the equation E = (hc)/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength). To determine if the light can cause the emission of electrons, we compare this energy to the work function of each metal: sodium (2.3 eV), cesium (2.1 eV), copper (4.7 eV), and iron (4.5 eV).

Using the photoelectric equation KEmax = E - Φ, where E is the energy of the incident photon and Φ is the work function, we can calculate the maximum kinetic energy (KEmax) of the emitted electrons:

• Sodium: KEmax = 3.1 eV - 2.3 eV = 0.8 eV
• Cesium: KEmax = 3.1 eV - 2.1 eV = 1.0 eV
• Copper and Iron do not emit electrons because their work functions are higher than the photon energy.

Therefore, sodium and cesium metals would emit electrons when illuminated with red light of 400 nm wavelength. For sodium, the maximum kinetic energy of the emitted electrons would be 0.8 eV, and for cesium, it would be 1.0 eV.