Discussion
What should be the energy required, if an electron is used as a probe for studying the nuclear structure, shape and distribution. (Consider nuclear radius is \(10^{-13}\) cm) :
Answer: B
On the key, the electron needs an energy of about 0.2 GeV.
To resolve structure of size R, the probe's reduced de Broglie wavelength must be no larger than R, so \(p \approx \hbar/R\). At these energies the electron is ultra-relativistic and E = pc:
\[ \begin{aligned} E &\approx \frac{\hbar c}{R} = \frac{197\ \text{MeV fm}}{1\ \text{fm}} \\ &\approx 0.2\ \text{GeV} \end{aligned} \]
using \(R = 10^{-13}\) cm = 1 fm. Using the full wavelength \(\lambda = h/p\) instead would give about 1.2 GeV, which is not offered; the key's estimate is the order of magnitude used in electron-scattering experiments such as Hofstadter's. 0.1 GeV gives too long a wavelength, and 0.3 or 0.4 GeV are not what the estimate yields.
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