How do I find energy from wavelength, and wavelength of an electron?

Question

I missed two classes with strep, and this was covered in one of them. The book isn't working for me. Can someone walk me through, and give me an answer so I know that I'm doing it right? Please and thanks.

1) Green light has a wavelength of 5.0 x 10^2 nm. What is the energy, in joules, of one photon of green light? What is the energy, in joules, of 1.0 mol of photons of green light?

2) Calculate the wavelength of an electron with a mass of 9.11 x 10^-31 kg and a speed of 2.5 x 10^6 m.s^-1.

Answer 1

Oh wow, are you using Chemical Principles? Those questions look very familiar.

1.) Okay, so you have a wavelength of 5.0 x 10^ nm. All words in parenthesis are Greek letters that you should look up to know the symbols.

You have to first use the equation Wavelength(lambda) x Frequency(nu) = Speed of Light (c).

First you convert your wavelength 5.0 x10^2 nm to meters, in which case is 5.0 x 10^-7 meters. Then you find the frequency by rearranging the equation to

Frequency = Speed of Light/Wavelength

Speed of light is given in meters, 3.0 x 10^8 m/s. Divided by 5.0 x 10^-7 m, and you get 6.0 x 10^14 s^-1 (since seconds is in the denominator), which you can change to Hertz (Hz).

Now that you have frequency, you can use the equation

Energy (E) = Frequency (nu) x Planck's Constant (h)

So then you have

Energy = (6.0x10^14 Hz) x (6.626x10^-34 Joules seconds)

Planck's constant you can look up in the back of the book.

So the answer should turn out to be E = 3.976 x 10^-19 J. This value is for EACH individual photon. So you can use stoichiometry to find the total energy by using Avogadro's number. So

E(total) = 1.0 mol photons x (6.022x10^23 photons)/(1 mole photons) x (3.976 x 10^-19 J)/(1 photon)

Which you should get 2.4 x 10^5 Joules in total (significant figures here, there are 2 from the wavelength and moles of photons).

2.) For the wavelength, you have to use de Broglie's equation because you're given mass and speed. The de Broglie equation follows as

Wavelength (lambda) = Planck's Constant (h)/[Mass (kg) x Speed (m/s)]

So you can just plug into the equation to get

Wavelength = (6.626x10^-34 J s)/[(9.11 x 10^-31 kg) x (2.5 x 10^6 m/s)]

for which you should get

2.9 x 10^-10 meters, or 29 picometers for metric prefixes. There are two significant figures from the speed.

Answer 2

Energy From Wavelength

Answer 3

The formulas are
speed = frequency times wavelength
your speed is a constant and is always equal to 2.998 x 10^8
wavelength is usually given in nm, you whatever ur nm is, divide by 10^9 to get it in meters
Now plug them in and you get frequency. after u get that use
E = frequencyt times Plack's constant
Plack's constant is always 6.626 x 10^ - 34
So once you find frequency, you multiply that by plack's constant to get the energy. and that will be your answer in J per photon
to get it into Kj/mole, you simply divide by 1000 and mutliply by 6.022 x 10 ^23

1) divide 5.0 x 10^ 2 all by 10^ 9 to get it in nm
take 2.998 x 10^ 8 and divide by your wavelength which should be in meters, and u get frequency. then multiply that by 6.626 x 10^ - 34 for E in Joules per photon
now u want J per mole so you multitply by 6.022 x 10^ 23

2) And the second one just use Broglie relationship which someone already wrote
Good luck

Answer 4

1) Use E = h nu for energy per photon.

To find nu, use lambda x nu = speed (for any wavemotion) = c (for light). Remember to express lambda in m, because c is in m s-1

That's one photon. For a mole of them, just multiply by Avogadro's Number.

2) Use the de Broglie relationship

lambda x momentum = h

and momentum = mass x velocity

Definitions: lambda, wavelength; nu frequency, c speed of light, h Planck's constant.

Common trap: inconsistent units. Use SI units throughout.

You're all set!

Answer 5

Hope this helps!