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Chapter 7: Problem 8

(a) What is the frequency of light having a wavelength of \(456 \mathrm{nm} ?\) (b) What is the wavelength (in \(\mathrm{nm}\) ) of radiation having a frequency of \(2.45 \times 10^{9} \mathrm{~Hz}\) ? (This is the type of radiation used in microwave ovens.)

Short Answer

Expert verified
The frequency of light having a wavelength of \(456 nm\) is approximately \(6.58 \times 10^{14} Hz\). The wavelength of radiation having a frequency of \(2.45 \times 10^{9} Hz\) is approximately \(122.5 nm\).

Step by step solution

01

- Finding the Frequency

Using the relation \(c = \lambda \nu\), we want to solve for \(\nu\). So, we get \(\nu = \frac{c}{\lambda}\). We know that \(\lambda = 456 nm = 456 \times 10^{-9} m\) and \(c \approx 3.0 \times 10^8 m/s\). Substituting these values, we get: \(\nu = \frac{3.0 \times 10^{8}}{456 \times 10^{-9}} Hz\).
02

- Finding the Wavelength

In this part, we want to find the wavelength \(\lambda\) using the same formula. Thus, we obtain \(\lambda = \frac{c}{\nu}\). Given that \(c \approx 3.0 \times 10^8 m/s\) and \(\nu = 2.45 \times 10^9 Hz\), substituting these values in the equation gives us: \(\lambda = \frac{3.0 \times 10^{8}}{2.45 \times 10^{9}} m\). As the wavelength is asked in \(nm\), we convert the result to nanometers by multiplying it by \(10^9\).
03

- Calculating and Providing the Final Answers

By doing the actual calculations in Steps 1 and 2, we obtain the numerical values for the frequency and the wavelength, which represent the final answers to the problems.

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Most popular questions from this chapter

A photoelectric experiment was performed by separately shining a laser at \(450 \mathrm{nm}\) (blue light) and a laser at \(560 \mathrm{nm}\) (yellow light) on a clean metal surface and measuring the number and kinetic energy of the ejected electrons. Which light would generate more electrons? Which light would eject electrons with greater kinetic energy? Assume that the same amount of energy is delivered to the metal surface by each laser and that the frequencies of the laser lights exceed the threshold frequency.

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