What is the wavelength of a yellow light with a frequency of \( 5.2 \times 10^{14} \mathrm{~Hz} \) ? Give your answer in proper scientific notation \[ [?] \times 10^{[?]} \mathrm{m} \] 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 light, 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 of the light (\( 5.2 \times 10^{14} \, \mathrm{Hz} \)) Now, let's substitute the values into the formula and calculate the wavelength step by step. 1. Substitute the values into the formula: \[ \lambda = \frac{3.0 \times 10^{8}}{5.2 \times 10^{14}} \] 2. Perform the division of the coefficients and the subtraction of the exponents: \[ \lambda = \frac{3.0}{5.2} \times 10^{8 - 14} \] Now, let's calculate \( \frac{3.0}{5.2} \) and \( 8 - 14 \). Calculating \( \frac{3.0}{5.2} \): \[ \frac{3.0}{5.2} \approx 0.576923 \] And calculating \( 8 - 14 \): \[ 8 - 14 = -6 \] So, we have: \[ \lambda \approx 0.576923 \times 10^{-6} \] To express this in proper scientific notation, we can rewrite \( 0.576923 \) as \( 5.76923 \times 10^{-1} \): \[ \lambda \approx 5.76923 \times 10^{-1} \times 10^{-6} = 5.76923 \times 10^{-7} \] Now, rounding \( 5.76923 \) to three significant figures gives us \( 5.77 \). Thus, the wavelength of the yellow light is: \[ \lambda \approx 5.77 \times 10^{-7} \, \mathrm{m} \] In the required format, the coefficient is \( 5.77 \) and the exponent is \( -7 \). So, the final answer is: - Coefficient: \( 5.77 \) - Exponent: \( -7 \)