at what rate must electrons in a wire vibrate to emit microwaves with wavelength of 1.00 mm?

Answer 1

The equation to use is v=fλ where v is the speed of light, f is the frequency, i.e. the rate at which they vibrate, and λ is the wavelength in meters.

Rearrange the above equation and you get f=v/λ. So the answer is f=300000000/0.001 or 300GHz.

Answer 2

the wavelength does not depends on at what rate ,, rather it depends on with what speed the electrons are being emmitted....
Secondly microwaves have their own wavelength or frequency range..If the paricular wave or energy form is emiited at that wavelength then only microwaves will be emitted..Now this wavelength or frequency depends on the speed of the wave..e.g in case of current more the potential difference applied , more will be the speed of electrons, more will be the frequency and lesser wiil be the wavelength..

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Answer 3

Here is the formula: Wavelength (in Meters) = 300 / frequency in MHz

In your case, plug in what you know:
1 mm (.001 meters) = 300 / frequency in MHz.

With a little algebra, you can figure out the rest.

Answer 4

Microwaves are measured in NANOmeteres, NOT Millimeteres as you have suggested...

1 nanometere= 1,000,000 Millimeters