(a) What is the frequency of radiation that has a wavelength of 10 µm, about the size of a bacterium?

Question

Accepted Answer

Welcome back everyone in this example we need to calculate the frequency of a wave that has a wavelength of 50. So this is referring to a wave of light. And we want to recall that our symbol for frequency is the symbol here which is typically expressed in units of Hertz, which we should recall are equivalent to inverse seconds. So we can recall our formula for frequency where frequency is set equal to our speed of light, what will actually represent the speed of light by the color red. And this is then divided by our wavelength which we should recall is represented by the symbol lambda. Recall that wavelength is typically expressed in units of meters however, were given units of millimeters. So we need to convert from millimeters to meters. So plugging in what we know into our formula, we're going to say that our frequency is equal to and our numerator, let's recall that our speed of light is equal to the value 3. times 10 to the eighth Power meters per second. And in our denominator we have our wavelength which is given in the prompt as 50 millimeters, which we're going to again convert from millimeters in the dominator, two m in the numerator as our final unit. We're going to recall that our prefix milli tells us that we have 10 to the negative third power of our base unit meter equivalent to one millimeter. This allows us to cancel our units of millimeters, leaving us with meters as our final unit for our wavelength. And so now we can go ahead and cancel out meters in the numerator with meters in the denominator, leaving us with inverse seconds because seconds are in the denominator here as our final unit because it's meters per second. And so in our calculators, when we type in our quotient, we're going to yield a frequency equal to the value of six point oh times 10 to the ninth power and we have units of inverse seconds. But we can also recall that because it's equivalent to hurts, we can say or six point oh times 10 to the ninth power hurts is also a valid answer. And so we're going to go ahead and highlight our answer in inverse seconds since it corresponds the best with our prompt. And this is our final answer for our frequency of the wave with the corresponding wavelength. I hope that everything I explained was clear. If you have any questions, leave them down below and I'll see everyone in the next practice video.

(a) What is the frequency of radiation that has a wavelength of 10 µm, about the size of a bacterium?

Verified Solution

Key Concepts

Electromagnetic Spectrum

Wavelength and Frequency Relationship

Units of Measurement