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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The work function is given by:$$\phi = hf - KE_{max}$$where:* $\phi$ is the work function* $h$ is Planck's constant* $f$ is the frequency of the light* $KE_{max}$ is the maximum kinetic energy of the ejected electronsWe can convert the wavelength of the light to frequency using the equation:$$c = f\lambda$$where:* $c$ is the speed of light* $\lambda$ is the wavelength of the lightSubstituting the given values into the equations above, we get:$$f = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \text{ m/s}}{240 \times 10^{-9} \text{ m}} = 1.25 \times 10^{15} \text{ Hz}$$$$\phi = hf - KE_{max} = (6.626 \times 10^{-34} \text{ J s})(1.25 \times 10^{15} \text{ Hz}) - (2.58 \times 16.0 \times 10^{-19} \text{ J}) = 4.26 \times 10^{-19} \text{ J}$$Converting to eV, we get:$$\phi = \frac{4.26 \times 10^{-19} \text{ J}}{16.0 \times 10^{-19} \text{ J/eV}} = 2.66 \text{ eV}$$Therefore, the work function of the material is 2.66 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 $2.58 \mathrm { eV }$