- #1
crybllrd
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Homework Statement
the wavelength of the probing beam must be approximately the same as the size of objects we want to resolve. For each of the accelerators described below, determine the smallest size objects that are resolvable and name an object roughly that small, remembering that these are order-of-magnitude estimates.
(a) In the radioactive decay of radium, most emitted [tex]\alpha[/tex]particles (4He nuclei) travel at 1.5 ×10^7 m/s. This is what was used in the Geiger-Marsden Experiment.
(there are actually four questions, but I am trying to make sure I am on the right track)
Homework Equations
p=[tex]\frac{mv}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/tex]
p=[tex]\frac{h}{\lambda}[/tex]
[tex]\lambda[/tex]=[tex]\frac{h}{p}[/tex]
where h = Planck's constant
The Attempt at a Solution
Sorry, I am not too good with LATEX references...
a) v= 1.5e7 m/s
m=6.64e-27 kg
p=[tex]\frac{(6.64e-27 kg)(1.5e7 m/s)}{\sqrt{1-\frac{(1.5e7 m/s)^{2}}{3e8m/s^{2}}}}
[/tex]
I solve this equation to get momentum 9.97e20 kg*m/s, then plug it into the next formula to find the wavelength:
[tex]\lambda[/tex]=[tex]\frac{6.626 J*s}{9.97e20 kg*m/s}[/tex]
I get this answer:
[tex]\lambda[/tex]=6.65e-55
which is much smaller than an electron, quark or a string.
Surely I did something wrong, but I can't find my mistake.