The work function of sodium metal is 4.41 ×10^-19 J. If photons of wavelength 300 nm are incid

step 1 In question 12 of chapter 2, structure of atom of section 2, topic to advancement towards quantu

The work function of sodium metal is 4.41 ×10^-19 J. If...

The work function of sodium metal is $4.41 \times 10^{-19} \mathrm{~J}$. If photons of wavelength $300 \mathrm{~nm}$ are incident on the metal, the kinetic energy of the ejected electrons will be $\left(h=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s} ; c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)$ $\times 10^{-21} \mathrm{~J}$

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Key Concepts

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are ejected from a material surface when it is exposed to electromagnetic radiation of sufficient energy. This effect provided crucial evidence for the quantized nature of light and was instrumental in the development of quantum mechanics.

Photon Energy

Photon energy is the energy carried by a single photon and is determined by the equation E = hc/?, where h is Planck's constant, c is the speed of light, and ? is the wavelength of the photon. This relationship shows that shorter wavelengths correspond to higher photon energies.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. In the context of the photoelectric effect, a photon must have an energy greater than or equal to the work function for an electron to be ejected from the material.

Kinetic Energy Calculation

The kinetic energy of the ejected electrons is calculated by subtracting the work function from the energy of the incident photon. This calculation demonstrates the energy conversion where any energy excess beyond what is required to overcome the work function is imparted as kinetic energy to the electron.

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