Wavelength, Frequency, and Planck's Constant

Soaring Crane

1) What is the wavelength (in meters) of an electromagnetic wave of frequency 2812571875.00MHz?
Example: 1.11e-5
LAMBDA = c/v
=(3.00*10^8 m/s)/(2812571875.00MHz*10^6 Hz/MHz) = 1.07E-7 m??

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2) What is the wavelength (in meters) of an electromagnetic wave of frequency 7084.00MHz?
LAMBDA = c/v
=(3.00*10^8 m/s)/(7084.00MHz*10^6 Hz/MHz) = 4.23E-1 m??

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3) How much energy is carried by a mole of photons with frequency 704.00MHz?
Give your answer in kilojoules per mole, Example: 1.11e-5
Careful with your conventions.
E = hv
=(6.626*10^-34)*(704.00MHz*10^6 Hz/MHz) = 4.665E-25 J
4.665E-25 J(1 kJ/10^-3 J)* (6.02*10^23 photons/1mol) = 2.81E-4 kJ/mol??
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Did I express my answers with the right significant digits and calculations?
Thanks.

Pengwuino

Yes, the significant digits look correct and the calculations seem correct although I don't have a calculator around at the moment.

Integral

You are given a lot of signifiant digits in your problem, why did you only use 3 for c? Is that c to 3 digits? There are about 8 digits of c available, why not use them?

Pengwuino

I suppose its because he's using a text book and I bet he might get the answers wrong (as far as grading is concerned) if he starts using different sources for the numbers.

Ouabache

If your text does give constant c to more significant digits, I would use them as Integral suggests. If you are not given speed of light in your text, you can use any valid source such as NIST (national institute of standards & technology). An equally correct answer to this part is 107nm. If your question does not specify units for your answers, both solutions are good.

I would check this again, especially your decimal place.

Your solution is correct but your equation is not...
You should have (1 kJ/10^3J), using your equation as written, you would get 281 kJ/mol

Soaring Crane

For #2, it is 4.23E-2 m?
For the constant c, my textbook gives the value in 8 decimal places, but it says that it is mostly rounded off to 3.00*10^8 and it uses this rounded off version in examples.

Ouabache

Nice job on #2 !! Try solving your questions, more than one way. Then you will be able to catch things like this on your own.

If they use the rounded off version of c in their examples, for practical purposes, you probably can use it as well. If you're in doubt, ask your teacher first before handing in those questions..