**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) \[ \lambda = \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \] \[ \text{nm} \]

Arrange the following regions of the electromagnetic spectrum in order of decreasing wavelength: microwaves, visible light, UV light, inferred radiation, X-rays.

A highly excited atom of hydrogen makes a transition from the n = 10 to the n = 9 state and emits a photon. What is the wavelength in meters of the photon emitted when this highly excited hydrogen atom of hydrogen makes its transition from the n = 10 to the n = 9 state?

At the Cincinnati zoo you can see the 45.4 kg cheetah run and it flew across the pen at 65.4 miles per hour – your  super de Broglie powers of observation allowed you to notice that the de Broglie wavelength of the cheetah was what (in units of meters)? Pay attention to units! Note: 1609 meters = 1 mile

What is the wavelength (in meters) of a photon that has a frequency of 7.46x1014 hertz. Recall that photons travel at the speed of light. Express your answer in Scientific Notation.

A laser pointer used in the classroom emits light at 4950 Å, at a power of 4.00 mW. (One watt is the SI unit of power, the measure of energy per unit of time. 1 W = 1 J/s). How many photons are emitted from the pointer in 115 seconds?

Infrared radiation from young stars can pass through the heavy dust clouds surrounding them, allowing astronomers here on Earth to study the earliest stages of star formation, before a star begins to emit visible light. Suppose an infrared telescope is tuned to detect infrared radiation with a frequency of 13.6THZ. Calculate the wavelength of the infrared radiation. Round your answer to 3 significant digits. um

Microwaves are a form of electromagnetic radiation with wavelengths between 1 mm and 1 m. What is the frequency of a microwave with a wavelength of 3.52mm?

A radiowave has a frequency of 94.9 MHz.  Calculate the wavelength of this frequency, in meters.  Provide your answers in three sig figs.

Gamma radiation has frequencies in the 1020 Hz range. What is the wavelength in meters of gamma radiation with a frequency of 8.19 x 1020 Hz?