Hi, This is one of my chem hw problems. Does anyone have links to websites that might help me solve this..or equations? It sounds like there are two parts to the question but I'm not sure. Volts and Joules?
1. Electrons are used to determine the structure of crystal surfaces. To have diffraction, the
wavelength, λ, of the electrons should be on the order of the lattice constant, which is typically 0.30
nm. What energy do such electrons have, expressed in electron-volts and joules?
Expressed in joules.
E = hc/lambda.
E will be in joules. h is Planck's constant, c is speed of light in m/s, and lambda is in meters. Convert 0.3 nm to meters which will be 0.3 x 10^-9 m. You can look in your text, often on the inside of front OR back cover, for joules to ev conversion factor.
Thanks!
To solve this problem, we need to relate the wavelength of the electrons with their energy. We can use the equation for the energy of a photon in terms of its wavelength:
E = hc / λ
where E is the energy, h is Planck's constant (6.63 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength.
1. Let's start by converting the given lattice constant from nanometers (nm) to meters (m):
0.30 nm = 0.30 x 10^-9 m
2. Now, we can substitute the wavelength into the energy equation and solve for the energy:
E = (6.63 x 10^-34 J·s)(3.00 x 10^8 m/s) / (0.30 x 10^-9 m)
E = 6.63 x 10^-34 J·s x 3.00 x 10^8 m/s / 0.30 x 10^-9 m
After performing the calculations, we get the energy in joules.
3. To express the energy in terms of electron-volts (eV), we can use the conversion factor where 1 electron-volt is equal to 1.6 x 10^-19 joules:
Energy (in eV) = Energy (in J) / (1.6 x 10^-19 J/eV)
By following these steps, you can calculate the energy of the electrons in both electron-volts and joules.