Achieve question #13

[Xinyue Zou 2K]

For the question: The E. coli bacterium is about 2.3 μm long. Suppose you want to study it using photons of that wavelength or electrons having that de Broglie wavelength. What is the energy Eelectrion of the electron?
How would we find the E for the electron?

[Katelyn Alvarado 3K]

You would use the equation c=wavelength times frequency to convert from wavelength to frequency and then use energy = planck's constant times frequency to get to your energy. However, before doing both of these steps you need to make sure you convert from micrometers to meters using the conversion 1 micrometer = 10^-6 meters.

[Alyssa Ly 2G]

Hello!

To find the energy of the electron, you can use the equations Kinetic Energy = (1/2)mv^2 and deBrogile's equation wavelength = h/p = h/(mv). The formula KE = (1/2)mv^2 can be used to find the energy of the electron. However, first, the velocity has to be found in order to use the KE energy. To do this, use the deBrogile equation.

wavelength = h/(mv) --> 1/wavelength = (mv)/h --> (h/wavelength) = (mv) --> v = h/[(wavelength)(m)]

v = (6.63 x 10^-34 Js)/[(2.3 x 10^-6 m)(9.11 x 10^-31)]

After finding the velocity, the value can be plugged into the KE equation.

KE = (1/2)(9.11 x 10^-31 kg)(velocity found above)^2 = Energy of electron!

I hope this was helpful! :D

[Alexander Moroz 1B]

To find energy of photons, we can use E=hv, but to find energy of electrons we need to use the kinetic energy equation KE=1/2mv^2.

However, we are missing velocity. To find it, we can use de Broglie's equation wavelength=h/mv.

First convert 2.3 micrometer to regular meters using conversion 1m=1e-6 microm.

Plug in wavelength and plank's constant, as well as the mass of an electron given on our formula sheet and solve for velocity, which can be plugged in to find the energy of an electron with 2.3 micrometer wavelength.

Do not confuse photon equations with electron equations!
Any time you are solving for electrons, the equation will have mass and velocity in them, while photon equations will have the speed of light constant, c, and frequency.