What is the frequency of yellow light with an energy of \( 3.4 \times 10^{-19} \mathrm{~J} \) ? \[ \begin{array}{c}\mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \\ {[?] \times 10^{[?]} \mathrm{Hz}}\end{array} \]

To determine the frequency (\( f \)) of yellow light with an energy (\( E \)) of \( 3.4 \times 10^{-19} \) joules, you can use the relationship between energy and frequency given by Planck's equation: \[ E = h \cdot f \] Where: - \( E \) is the energy of the photon, - \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \mathrm{J \cdot s} \)), - \( f \) is the frequency of the light. Rearranging the equation to solve for \( f \): \[ f = \frac{E}{h} \] Plugging in the known values: \[ f = \frac{3.4 \times 10^{-19} \, \mathrm{J}}{6.626 \times 10^{-34} \, \mathrm{J \cdot s}} = \frac{3.4}{6.626} \times 10^{(-19) - (-34)} \, \mathrm{Hz} \] \[ f \approx 0.513 \times 10^{15} \, \mathrm{Hz} \] This can be expressed in standard scientific notation as: \[ f \approx 5.13 \times 10^{14} \, \mathrm{Hz} \] **Final Answer:** The frequency of the yellow light is \( 5.13 \times 10^{14} \) Hz.