How Much Kinetic Energy Do Electrons Need to Resolve a 10fm Nucleus?

AI Thread Summary
To resolve a nucleus of size 10 femtometers (fm), the kinetic energy required for electrons is calculated using the de Broglie wavelength equation. The initial calculations yielded 1.50 x 10^10 eV and 124 MeV, but the correct answer is 1240 MeV. The discrepancy suggests that a relativistic approach may be necessary, as the kinetic energy of the electron exceeds its rest energy. The discussion emphasizes the importance of using appropriate equations to account for relativistic effects in high-energy scenarios. Accurate calculations are crucial for understanding particle interactions at such small scales.
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Homework Statement


To "obeserve" small objects,one measures the diffraction of the particles whose de Broglie wavelength is approximately equal to the object's size.
Find the kinetic energy(in electron volts) required by the electrons to resolve
c) a nucleus of size 10fm.


Homework Equations


I use the de broglie equation
~ = wavelenth
~= h/(2MeEk)^1/2
the ans i found is 1.50x10^10 eV
and energy-momentum conservation
E2=p2c2+Me2c4
but I can't find the correct answer for it
the ans i found is 124MeV

the real ans given is 1240Mev
is there any way to find it??
 
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I get the same answer you do.
 
does tat mean something wrong with the ans given??
or i should use relativistic formula since the kinetic energy of electron is larger thn rest energy of electron?
 
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