**Transcription for Educational Website** --- **Part A: Problem Statement** A microwave oven operates at a frequency of 2.20 GHz. What is the wavelength of the radiation produced by this appliance? *Express the wavelength numerically in nanometers.* **Hints** - You can view available hints by expanding the "View Available Hint(s)" section. **Calculation Equation Input Section** λ = [ ] nm **Explanation** In this problem, you are asked to calculate the wavelength of a microwave radiation, given its frequency. Utilize the formula relating speed of light, frequency, and wavelength: \[ c = \lambda \nu \] Where: - \( c \) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)) - \( \lambda \) is the wavelength - \( \nu \) is the frequency To find the wavelength (\( \lambda \)) in nanometers, rearrange the formula: \[ \lambda = \frac{c}{\nu} \] Convert the units as necessary to express the wavelength in nanometers. **Note** Ensure the frequency is correctly converted to compatible units when applying the formula. The result will give you the wavelength in meters, which can then be converted to nanometers by multiplying by \(10^9\). --- **Electromagnetic Radiation** Electromagnetic radiation behaves both as particles (called *photons*) and as waves. Wavelength (\(\lambda\)) and frequency (\(\nu\)) are related according to the equation: \[ c = \lambda \times \nu \] where \( c \) is the speed of light (3.00 x 10\(^8\) m/s). The energy (\( E \) in joules) contained in one quantum of electromagnetic radiation is described by the equation: \[ E = h \times \nu \] where \( h \) is Planck’s constant (6.626 x 10\(^{-34}\) J·s). Note that frequency has units of inverse seconds (s\(^{-1}\)), which are more commonly expressed as hertz (Hz). --- **Part A** A microwave oven operates at 2.20 GHz. What is the wavelength of the radiation produced by this appliance? **Express the wavelength numerically in nanometers.** View Available Hint(s) \[ \lambda = \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \] \[ \text{nm} \]