To calculate the energy of an electron in the second shell of a hydrogen atom, we focus on its potential energy, which can be expressed using the formula:

$\Delta E = -R \cdot \frac{Z^2}{n^2}$

In this equation, $\Delta E$ represents the change in energy, $R$ is the Rydberg constant, $Z$ is the atomic number, and $n$ is the principal quantum number corresponding to the energy level or shell number.

For hydrogen, the atomic number $Z$ is 1. The Rydberg constant $R$ is approximately $-2.178 \times 10^{-18}$ joules. Since we are interested in the second shell, we set $n = 2$. Plugging these values into the formula gives:

$\Delta E = -(-2.178 \times 10^{-18}) \cdot \frac{1^2}{2^2}$

Calculating $1^2$ yields 1, and $2^2$ yields 4. Thus, the equation simplifies to:

$\Delta E = -2.178 \times 10^{-18} \cdot \frac{1}{4}$

This results in:

$\Delta E = -5.445 \times 10^{-19}$ joules

When reporting this value, it is important to consider significant figures. In this case, using four significant figures is appropriate, leading to the final energy of the electron in the second shell of the hydrogen atom being approximately:

$\Delta E \approx -5.445 \times 10^{-19}$ joules