Measuring Nuclear Radius

\(\(\text{Initial } E_{k}=E_{\text{elec}}=\frac{Q_{\text{nucleus}q_{\text{alpha}}}}{4\pi\varepsilon_{0}r}\)\)
- \(E_{\text{elec}}\) is electric potential energy
- \(\varepsilon_{0}\) is the permittivity of free space
- \(Q_{\text{nucleus}}\) is the charge on the nucleus
- \(q_{\text{alpha}}\) is the charge on the alpha particle
- \(r\) is how close the particle can get to the nucleus

\(\(\lambda \approx \frac{hc}{E}\)\)
- \(\lambda\) is the de broglie wavelength
- \(h\) is the plank constant
- \(c\) is the speed of light
- \(E\) is the energy of the electron

\(\(\sin\theta \approx \frac{1.22\lambda}{2R}\)\)
- \(\theta\) is the scattering angle
- \(\lambda\) is the wavelength
- \(R\) is the radius of the nucleus that the electrons have been scattered by