Calculate the energy associated with an electron in the first orbit...

The energy of an electron in the $n^{\text{th}}$ orbit of a hydrogen-like species is given by the Bohr model as:

$E_n = -2.18 \times 10^{-18} \times \dfrac{Z^2}{n^2}\ \text{J}$

For a hydrogen atom, the atomic number $Z = 1$.

For the first orbit, the principal quantum number $n = 1$.

Substituting these values into the formula, we get:

$E_1 = -2.18 \times 10^{-18} \times \dfrac{1^2}{1^2}\ \text{J}$

$E_1 = -2.18 \times 10^{-18}\ \text{J}$

Answer: $-2.18 \times 10^{-18}\ \text{J}$