Calculating Energy of Mono-energetic Electrons Diffracted by a Lattice

[Master J]

Homework Statement

"Mono-energetic electrons are diffracted by a lattice. Their wavelength is shown to be L=0.35nm. What are the energies of the electrons?"

Homework Equations

E=hf

c=hL

The Attempt at a Solution

c/L gives 8.566exp17

h=6.626exp-34

I plug them in and get: 5.66exp-19 J

The answer is 1184.4 kJ mol -1.

So I divide my answer by 1000, and multiply it by Avogadros number. But my answer is nowhere near the actual answer. Where am I going wrong?

 

[anathema]

Thank you for your question. It seems that you have made a small mistake in converting your answer to the correct units. When calculating the energy of the electrons using the equation E=hf, you correctly used Planck's constant (h) and the wavelength (L) to find the energy in joules (J). However, when converting to the correct units of kilojoules per mole (kJ/mol), you divided by 1000 (to convert from joules to kilojoules) and then multiplied by Avogadro's number (to convert from joules per molecule to joules per mole). This is incorrect because Avogadro's number is already included in the units of kJ/mol.

To convert from joules to kilojoules per mole, you only need to divide your answer by 1000. Therefore, the correct answer is 5.66 x 10^-22 kJ/mol. I hope this helps clarify your mistake. Keep up the good work in your studies!

 

[Moetasim]

I would like to point out that your attempt at a solution is incorrect. The equations you have used are for calculating the energy of photons, not electrons. The correct equation for calculating the energy of an electron is E= (h^2)/2m * (2π/L)^2, where h is the Planck's constant, m is the mass of the electron, and L is the wavelength.

In order to calculate the energy of the electrons, you need to know the mass of the electron and the value of Planck's constant. Once you have those values, you can plug them into the equation and solve for the energy. The result will be in joules (J). To convert it to kilojoules (kJ) per mole, you will need to divide by Avogadro's number (6.02 x 10^23).

Therefore, in order to accurately calculate the energy of the electrons, you will need to provide the mass of the electron and the value of Planck's constant. Without those values, it is not possible to accurately solve for the energy.