Sapling HW Question 25

[Nayra Gharpetian 3F]

Hi I can't figure out how to solve the second part to this problem. The problem says:

The E. coli bacterium is about 1.7 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?
What is the energy E electron of the electron?

I was able to calculate the energy of the photon but I don't know how to calculate the energy of the electron without being given the velocity.

[Jeffrey Doeve 2I]

You could solve for the energy of the electron by using its De Broglie Wavelength. Knowing the electron's wavelength would allow you to solve for velocity in the De Broglie Wavelength equation. Then, you would be able to plug the velocity of the electron into the kinetic energy formula to find the energy of the electron. Hope this helps!

[Gina Spagarino 3G]

To calculate the energy of the electron, use DeBroglie's: lambda=h/p (with lamda as the bacterial length)... and then use ((the p you solved for)/(electron mass)) as the velocity [p=mv so v=p/m]

[Lea Chamoun 2J]

The question says that the electrons have de Broglie wavelength of 1.7 μm. First, convert 1.7 μm to meters (1 μm= 10^-6m). Since λ= h/mv, then v=h/mλ. You can solve for v now because the wavelength, mass, and Planck's constant are given. Once you have found in the velocity, you can find the kinetic energy of the electron using E= 1/2mv^2

[Sukhkiran Kaur 3I]

Hi! To solve this I first converted the wavelength from μm to m by multiplying 1.7 by 10^-6. Then, you can solve for v by using the equation v=h/mλ. Plug in the given mass, wavelength and Planck's constant, and then use the calculated velocity to find the KE using E=0.5mv^2.

[Gian Boco 2G]

You can find the velocity based because you know the wavelength and mass values. So, isolate v in wavelength = h/mv and plug it into 1/2 mv^2.

[Ralph Zhang 2L]

The key is to use electron's mass, which is given on the equation sheet, and plug that into De Broglie's equation to find the velocity.

[Maddie Turk Disc 2J]

Thank you so much! I think I was forgetting to convert from um to m which was throwing me off, great explanation!

[Maddie Turk Disc 2J]

For the equation 1/2 mv^2 is the quantity mv raised to the second power or just v?