Homework Week 2 Question 13

[Maggie Messer 1A]

Hi can someone help me on how I'm supposed to start with this problem?

The E coli bacterium is about 1.6 μm long. Suppose you want to study it using photons of that wavelength or electrons having that de Broglie wavelength.

What is the energy E photon of the photon?

[Ashley M 2E]

Use the equation of E(photon) = hc/(wavelength) to find the energy of the photon. You can get this equation by combining E = hv and c = (wavelength)(v). The length of the bacterium is pretty much irrelevant; it is merely giving you the wavelength that they want you to use to plug in and find the energy.

[SarahOMalley1D]

Hi! To study the makeup of something (e.g. a crystal, a metal, etc), the wavelength of photons you're inserting has to be about the same size as what you're studying or the gaps between each particle of what you're studying. In order to study the makeup of an E-coli bacterium, your light's wavelength has to be the size of a bacterium or smaller, so you must find the energy per photon of light that corresponds to this wavelength. Hopefully, this explanation helps the math of this question make a little more sense.

[Kiku Shirakata 2A]

Hello,
As Ashley mentioned above, you should use the equation E(photon) = hc/(wavelength) to find the energy of the photon as the question asks. For the second part of the problem, it asks to find the energy of the electron. For this part, use velocity = h/(m*wavelength) to find the velocity of the electron, then use the E(kinetic)=0.5mv^2 equation to find the energy of the electron
Hope this helps!

[Sarah Wang 1I]

You didn't ask for how to begin approaching finding the E of the electron, but in case you forgot to include that part in the question, here's a brief rundown! We can use the formula E_k = 1/2 * m * v^2 because the electron is moving and its energy is kinetic. The velocity is calculated using deBroglie's equation after plugging in Planck's constant and the wavelength. The mass of an electron is 9.11x10^-31 kg. Then plug these components into the formula and you have your answer!