What's the Minimum Energy of a Wave Needed to View a 0.1 nm Particle?

[teclordphrack]

I have a problem that ask for the minimum energy of a wave that we will use to see a particle of size .1 nm. I understand that I can not see a .1 nm particle with any wave length larger than .1 nm. I thought this would be easy and I would use De Broglis relation of electron waves. (f=E/h) or E=fh=hc/λ. Using this I get 12400eV... this is the wrong answer.

What the book says to do is use an eqn. "wavelength associated with a particle of mass M.

it is: λ=hc/sqrt(2mc^2K) OR for my specific case: λ=1.226/sqrt(K) nm

This second equation , if I am correct, is getting the kinetic energy of the wavelength, not the total energy.

I do not understand what I should be looking for in problems asking for energy of wavelengths to distinguish the use of the first eqn I presented Vs the second one. Any enlightenment on this area would be appreciated.

 

[Bill_K]

I get 12400eV... this is the wrong answer.

That's what I get too. What do you think it should be?

 

[teclordphrack]

you have to use λ=hc/sqrt(2Kmc^2). The answer is 150eV and is rounded to .2KeV because of sig figs with the .1nm. There is something to do with non/relative particles, i think. That you use to determine which of the 2 equations to use.

 

[KWillets]

What is K?

 

[mfb]

E=fh=hc/λ would assume that the electrons move at the speed of light. For 1nm, they are slow and non-relativistic formulas can be used. 1/2mv^2=E, λ=v/f=vh/E. Solving this for λ(E) should give the formula in post 3.

 

[KWillets]

[You're using the equation for frequency, not wavelength. The reason that's difficult is that phase velocity is not constant, so you can't just use the inverse as the wavelength. De Broglie derived the dispersion relation v_group*v_phase = c², where v_group is the particle velocity.