What is the wavelength of a UV light with a frequency of \( 8.8 \times 10^{17} \mathrm{~Hz} \) ? Give your answer in proper scientific notation. \[ [?] \times 10^{[?]} \mathrm{m} \] \( \quad c=3.0 \times 10^{8} \mathrm{~m} / \mathrm{s} \) Enter the coefficient in the green box and the exponent in the yellow box.

To find the wavelength (\( \lambda \)) of UV light given its frequency (\( f \)), we can use the formula: \[ \lambda = \frac{c}{f} \] where: - \( c \) is the speed of light (\( 3.0 \times 10^{8} \, \mathrm{m/s} \)) - \( f \) is the frequency (\( 8.8 \times 10^{17} \, \mathrm{Hz} \)) Now, let's calculate the wavelength step by step. 1. Substitute the known values into the formula: \[ \lambda = \frac{3.0 \times 10^{8} \, \mathrm{m/s}}{8.8 \times 10^{17} \, \mathrm{Hz}} \] 2. Perform the division: \[ \lambda = \frac{3.0}{8.8} \times \frac{10^{8}}{10^{17}} \] 3. Calculate \( \frac{3.0}{8.8} \): \[ \frac{3.0}{8.8} \approx 0.340909 \] 4. Calculate \( \frac{10^{8}}{10^{17}} \): \[ \frac{10^{8}}{10^{17}} = 10^{8-17} = 10^{-9} \] 5. Combine the results: \[ \lambda \approx 0.340909 \times 10^{-9} \, \mathrm{m} \] 6. Convert \( 0.340909 \) into proper scientific notation: \[ 0.340909 = 3.40909 \times 10^{-1} \] 7. Therefore, we can express \( \lambda \) as: \[ \lambda \approx 3.40909 \times 10^{-1} \times 10^{-9} = 3.40909 \times 10^{-10} \, \mathrm{m} \] Now, rounding \( 3.40909 \) to three significant figures gives us \( 3.41 \). Thus, the final answer in scientific notation is: \[ \lambda \approx 3.41 \times 10^{-10} \, \mathrm{m} \] So, the coefficient is \( 3.41 \) and the exponent is \( -10 \).