Determine the shortest frequency of light required to remove an electron from a sample of Ti metal if the binding energy of titanium is 3.14 × 10³ kJ/mol. A) 7.87 × 10¹⁵ Hz B) 4.74 × 10¹⁵ Hz C) 2.11 × 10¹⁵ Hz D) 1.27 × 10¹⁵ Hz E) 6.19 × 10¹⁵ Hz

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Quizplus · Accepted Answer

To find the frequency of light required to remove an electron from titanium, we use the equation $E = h\nu$, where $E$ is the energy in joules, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{Js}$), and $\nu$ is the frequency in Hz. The binding energy given is in kJ/mol, so first, we convert it to joules per electron. $3.14 \times 10^{3} \, \text{kJ/mol} = 3.14 \times 10^{3} \times 10^{3} \, \text{J/mol}$. Since $1 \, \text{mol} = 6.022 \times 10^{23} \, \text{electrons}$, the energy per electron is $\frac{3.14 \times 10^{6} \, \text{J/mol}}{6.022 \times 10^{23} \, \text{electrons/mol}} = 5.21 \times 10^{-19} \, \text{J/electron}$. Using the equation $E = h\nu$, solving for $\nu$ gives $\nu = \frac{E}{h} = \frac{5.21 \times 10^{-19} \, \text{J}}{6.626 \times 10^{-34} \, \text{Js}} = 7.87 \times 10^{14} \, \text{Hz}$.

Determine the Shortest Frequency of Light Required to Remove an Electron