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Chapter 7: Problem 7

(a) What is the wavelength (in nanometers) of light having a frequency of \(8.6 \times 10^{13} \mathrm{~Hz} ?\) (b) What is the frequency (in Hz) of light having a wavelength of \(566 \mathrm{nm} ?\)

Short Answer

Expert verified
The wavelength of light having a frequency of \(8.6 × 10^{13} Hz\) is \(3.5 nm\), and the frequency of light having a wavelength of \(566 nm\) is \(5.3 × 10^{14} Hz\).

Step by step solution

01

Calculate Wavelength

Given a frequency of \(8.6 × 10^{13} Hz\), use the formula \(λ = c/f\). Replace \(c\) with \(3.0 × 10^8 m/s\) and \(f\) with the given frequency, \(8.6 × 10^{13} Hz\). Perform the calculation to find the wavelength in meters. Then, convert meters to nanometers by multiplying by \(1 × 10^{9}\), since 1 meter is equal to \(1 × 10^{9}\) nanometers.
02

Calculate Frequency

Given a wavelength of \(566 nm\), use the formula \(f = c/λ\). Replace \(c\) with \(3.0 × 10^8 m/s\) and convert the wavelength from nanometers to meters by multiplying by \(1 × 10^{-9}\), as \(1 nm = 1 × 10^{-9} m\). Perform the calculation to find the frequency in Hz.

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