When it is struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of $2.58 \mathrm { eV }$ What is the work function of this material? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 16.0 × 10^-19 J) A) 2.60 eV B) 2.18 eV C) 3.02 eV D) 3.43 eV

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Quizplus · Accepted Answer

The work function is given by the equation:$$K_{max} = hf - \phi$$where:* $K_{max}$ is the maximum kinetic energy of the ejected electrons* $h$ is Planck's constant* $f$ is the frequency of the incident photons* $\phi$ is the work functionWe can rearrange this equation to solve for the work function:$$\phi = hf - K_{max}$$Plugging in the given values, we get:$$\phi = (6.626 \times 10^{-34} \text{ J} \cdot \text{s})(3.00 \times 10^8 \text{ m/s})/(240 \times 10^{-9} \text{ m}) - (2.58 \text{ eV})(16.0 \times 10^{-19} \text{ J/eV})$$$$\phi = 8.31 \times 10^{-19} \text{ J} - 4.13 \times 10^{-19} \text{ J}$$$$\phi = 4.18 \times 10^{-19} \text{ J}$$Converting to eV, we get:$$\phi = 4.18 \times 10^{-19} \text{ J} \times (1 \text{ eV}/16.0 \times 10^{-19} \text{ J})$$$$\phi = 2.61 \text{ eV}$$Therefore, the work function of this material is 2.61 eV, which is closest to choice A, 2.60 eV.

When It Is Struck by 240-Nm Photons, a Metal Ejects 2.58eV2.58 \mathrm { eV }2.58eV

When It Is Struck by 240-Nm Photons, a Metal Ejects $2.58 \mathrm { eV }$