Question

Electromagnetic radiation behaves both as particles (called photons) and as waves. Wavelength (λ) and frequency (ν) are related according to the equation

c=λ×ν

where c is the speed of light (3.00×108 m/s). The energy (E in joules) contained in one quantum of electromagnetic radiation is described by the equation

E=h×ν

where h is Planck's constant (6.626×10−34 J⋅s). Note that frequency has units of inverse seconds (s−1), which are more commonly expressed as hertz (Hz).

A microwave oven operates at 3.00 GHz . What is the wavelength of the radiation produced by this appliance?
Express the wavelength numerically in nanometers.

Answer 1

The wavelength of the radiation produced by the microwave oven operating at 3.00 GHz is 10 mm or 10,000,000 nanometers. It can be done by convert meters to nanometers, we can multiply by 10^9.

Step-by-step explanation:

Electromagnetic radiation, such as light, behaves as both particles and waves. The wavelength (λ) and frequency (ν) of electromagnetic radiation are related by the equation c=λ×ν, where c is the speed of light. To find the wavelength of the radiation produced by a microwave oven operating at 3.00 GHz, we can rearrange the equation to solve for λ.

Since the speed of light is 3.00×10^8 m/s and the frequency is 3.00 GHz (3.00×10^9 Hz), we can substitute these values into the equation to calculate the wavelength numerically in meters. To convert meters to nanometers, we can multiply by 10^9. Therefore, the wavelength of the radiation produced by the microwave oven is 10 mm or 10,000,000 nanometers.

Or The microwave oven operates at a frequency of 3.00 GHz, which is equivalent to 3.00 × 109 Hz. To find the wavelength (λ) of the radiation produced by the microwave oven, we can rearrange the equation c = λ × ν to solve for λ: λ = c / ν. Using the speed of light (ν) as 3.00 × 108 m/s, the calculation yields λ = (3.00 × 108 m/s) / (3.00 × 109 Hz) = 0.1 meters, or 100 centimeters, which is 1x105 nanometers.