Question

what is the wavelength (in nm) of light having a frequency of 7.63 × 10¹³ hz? what is the frequency (in hz) of light having a wavelength of 9.00 × 10² nm? part 1 of 2 be sure your answer has the correct number of significant digits. wavelength of light: □ nm ×10^□ part 2 of 2 be sure your answer has the correct number of significant digits. frequency of light: □ hz ×10^□

Explanation:

Part 1: Wavelength Calculation

Step1: Recall the formula for light (c = λν)

The speed of light \( c = 3.00 \times 10^8 \, \text{m/s} \), frequency \(
u = 7.63 \times 10^{13} \, \text{Hz} \), and \( \lambda \) is wavelength. Rearranging \( \lambda = \frac{c}{
u} \).

Step2: Substitute values

\( \lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{7.63 \times 10^{13} \, \text{Hz}} \)
\( \lambda = 3.93184797 \times 10^{-6} \, \text{m} \)

Step3: Convert to nanometers (1 m = 10⁹ nm)

\( \lambda = 3.93184797 \times 10^{-6} \, \text{m} \times \frac{10^9 \, \text{nm}}{1 \, \text{m}} \)
\( \lambda = 3.93 \times 10^3 \, \text{nm} \) (3 significant digits)

Step1: Recall \( c = \lambda

u \), rearrange \(
u = \frac{c}{\lambda} \)
Wavelength \( \lambda = 9.00 \times 10^2 \, \text{nm} = 9.00 \times 10^2 \times 10^{-9} \, \text{m} = 9.00 \times 10^{-7} \, \text{m} \), \( c = 3.00 \times 10^8 \, \text{m/s} \)

Step2: Substitute values

\(
u = \frac{3.00 \times 10^8 \, \text{m/s}}{9.00 \times 10^{-7} \, \text{m}} \)
\(
u = 3.33333333 \times 10^{14} \, \text{Hz} \)

Step3: Round to 3 significant digits

\(
u = 3.33 \times 10^{14} \, \text{Hz} \)

Answer:

\( 3.93 \times 10^{3} \)

Part 2: Frequency Calculation