The work function of sodium metal is 2.3 eV. What is the longestwavelength light that can cause

step 1 Good day. The topic is about energy of a photon. Given with its wavelength, we solve for energy

The work function of sodium metal is 2.3 eV. What is the...

The work function of sodium metal is $2.3 \mathrm{eV}$. What is the longestwavelength light that can cause photoelectron emission from sodium? At threshold, the photon energy just equals the energy required to tear the electron loose from the metal. In other words, the electron's $\mathrm{KE}$ is zero and so $h f=\varphi$. Since $f=c / \lambda$ $$ \begin{array}{c} \phi=\frac{h \mathrm{c}}{\lambda} \\ (2.3 \mathrm{eV})\left(\frac{\left(1.602 \times 10^{-19} \mathrm{~J}\right.}{1.00 \mathrm{eV}}\right)=\frac{\left(6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{\lambda} \\ \lambda=5.4 \times 10^{-7} \mathrm{~m} \end{array} $$

The work function of sodium metal is $2.3 \mathrm{eV}$. What is the longestwavelength light that can cause photoelectron emission from sodium?
At threshold, the photon energy just equals the energy required to tear the electron loose from the metal. In other words, the
electron's $\mathrm{KE}$ is zero and so $h f=\varphi$. Since $f=c / \lambda$
$$
\begin{array}{c}
\phi=\frac{h \mathrm{c}}{\lambda} \\
(2.3 \mathrm{eV})\left(\frac{\left(1.602 \times 10^{-19} \mathrm{~J}\right.}{1.00 \mathrm{eV}}\right)=\frac{\left(6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{\lambda} \\
\lambda=5.4 \times 10^{-7} \mathrm{~m}
\end{array}
$$

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Key Concepts

Threshold Condition

The threshold condition in the context of the photoelectric effect occurs when the energy of the incoming photon is exactly equal to the work function of the metal. At this point, the emitted electron has zero kinetic energy, and any additional energy from the photon would translate into kinetic energy of the electron.

Photoelectric Effect

The photoelectric effect is the phenomenon in which electrons are emitted from a material when it absorbs light (or more generally, electromagnetic radiation) of sufficient energy. This effect provided early evidence for the quantum nature of light and led to the development of quantum mechanics.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a key parameter in the photoelectric effect which determines the threshold frequency or wavelength of the incident light needed to eject electrons.

Planck's Equation

Planck's equation relates the energy of a photon to its frequency or wavelength through the equation E = h*f or equivalently E = h*c/?, where h is Planck's constant and c is the speed of light. This fundamental relationship is essential in calculating the energy carried by electromagnetic radiation.

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