How Can We Compare the Frequency and Wavelength of Gamma Rays and Visible Light?

[Allen J]

Hi, I am trying to solve a couple of questiosn where I need to say whether gamma rays have a higher frequency than visible light or not. The answer is obviously yes(they mentioned it several times in the text), but they want me to explain my answer based on the relationship between energy and frequency. Maybe they're referring to E=hf, but I'm not really sure how I could show anything with that anyway.

The second question wants to know which has the longer wavelength. Of course, the frequency and the wavelength are proportional. I could simply say this, based on the first question. But is there a way to answer it "properly", rather than say, "If the frequency is low, the wavelength is long; if the frequency is high, the wavelength is short" ?

 

[mathman]

For the first question, I presume they mean gamma rays have more energy than light, therefore have higher frequency.

For the second, wavelength is inversely proportional to frequency.

 

[Galileo]

Indeed, you can use E=hf. You'll have to know that gamma rays are much more energetic than visible light rays.

You know wavelength and frequency are inversely proportional. In fact, I`m sure you can state their precise relationship and deduce the answer from that. It doesn't get more proper than that.

 

[selfAdjoint]

Hi, I am trying to solve a couple of questiosn where I need to say whether gamma rays have a higher frequency than visible light or not. The answer is obviously yes(they mentioned it several times in the text), but they want me to explain my answer based on the relationship between energy and frequency. Maybe they're referring to E=hf, but I'm not really sure how I could show anything with that anyway.

Look up the energies of gamma rays and of the highest energy visible rays (violet) in your book. Perhaps there's a table or an annotated spectrum diagram? So then you can compare E_visible = hf_visible to E_gamma = hf_gamma and see which is bigger, and conclude which has higher frequency. You don't need to know h, but just that it's the same h for both frequencies.

The second question wants to know which has the longer wavelength. Of course, the frequency and the wavelength are proportional. I could simply say this, based on the first question. But is there a way to answer it "properly", rather than say, "If the frequency is low, the wavelength is long; if the frequency is high, the wavelength is short" ?

The relationship of frequency to wavelength is frequency = c/wavelength. Think of it this way; suppose the readiation was just successive spikes, like pickets of a picket fence going by you at a speed of c; one foot per nanosecond. Then the number of pickets per nanosecond going past is just the speed divided by the distance between them in feet. If they were half as far apart there'd be twice as many going by per nanosecond. Dimensionally, speed = length/time, and wavelength is length, so the quotient is 1/time {"per nanosecond"), which is the correct dimension for a frequency.

So you use that formula, freq = c/wavelength, to relate the frequency answer of the first question to the wavelength answer of the second one.