Chapter 40

Consider an atom with two closely spaced excited states \(A\) and \(B\). If the atom jumps to ground state from \(A\) or from \(B\), it emits a wavelength of \(500 \mathrm{~nm}\) or \(510 \mathrm{~nm}\), respectively. What is the energy difference between states \(A\) and \(B ?\)

In 1911, Ernest Rutherford modeled an atom as being a point of positive charge Ze surrounded by a negative charge \(-Z e\) uniformly distributed in a sphere of radius \(R\) centered at the point. At distance \(r\) within the sphere, the electric potential is $$ V=\frac{Z e}{4 \pi \varepsilon_{0}}\left(\frac{1}{r}-\frac{3}{2 R}+\frac{r^{2}}{2 R^{3}}\right) $$ (a) From this formula, determine the magnitude of electric field for \(0 \leq r \leq R .\) What are the (b) electric field and (c) potential for \(r \geq R\) ?