Question

what is the wavelength (in nm) of light having a frequency of ( 3.34 \times 10^{13} ) hz? what is the frequency (in hz) of light having a wavelength of ( 3.81 \times 10^2 ) nm? part 1 of 2 be sure your answer has the correct number of significant digits. wavelength of light: (square) nm part 2 of 2 be sure your answer has the correct number of significant digits. frequency of light: (square) hz

Explanation:

Part 1: Wavelength Calculation

Step1: Recall the formula \( c = \lambda

u \)
Where \( c = 3.00 \times 10^8 \, \text{m/s} \) (speed of light), \( \lambda \) is wavelength, and \(
u \) is frequency. Rearrange for \( \lambda \): \( \lambda = \frac{c}{
u} \)

Step2: Substitute values

\(
u = 3.34 \times 10^{13} \, \text{Hz} \), \( c = 3.00 \times 10^8 \, \text{m/s} \)
\( \lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{3.34 \times 10^{13} \, \text{Hz}} \)

Step3: Calculate wavelength in meters

\( \lambda = 8.982 \times 10^{-6} \, \text{m} \)

Step4: Convert meters to nanometers

\( 1 \, \text{m} = 10^9 \, \text{nm} \), so \( \lambda = 8.982 \times 10^{-6} \, \text{m} \times \frac{10^9 \, \text{nm}}{1 \, \text{m}} = 8.98 \times 10^3 \, \text{nm} \) (3 significant digits)

Step1: Use \( c = \lambda

u \), rearrange for \(
u \): \(
u = \frac{c}{\lambda} \)

Step2: Convert wavelength to meters

\( \lambda = 3.81 \times 10^2 \, \text{nm} = 3.81 \times 10^2 \, \text{nm} \times \frac{10^{-9} \, \text{m}}{1 \, \text{nm}} = 3.81 \times 10^{-7} \, \text{m} \)

Step3: Substitute values

\( c = 3.00 \times 10^8 \, \text{m/s} \), \( \lambda = 3.81 \times 10^{-7} \, \text{m} \)
\(
u = \frac{3.00 \times 10^8 \, \text{m/s}}{3.81 \times 10^{-7} \, \text{m}} \)

Step4: Calculate frequency

\(
u = 7.87 \times 10^{14} \, \text{Hz} \) (3 significant digits)

Answer:

\( 8.98 \times 10^3 \)

Part 2: Frequency Calculation