To solve this problem, we need to understand the energy dynamics of an electron in a Bohr orbit.$\\$In the Bohr model of the hydrogen atom, the total energy $(E)$ of an electron in orbit is given by:$\\ E = -\frac{k e^2}{2r} \\$where $k$ is Coulomb's constant, $e$ is the charge of the electron, and $r$ is the radius of the orbit.$\\$The kinetic energy $(K)$ of the electron is given by:$\\ K = \frac{k e^2}{2r} \\$The potential energy $(U)$ is given by:$\\ U = -\frac{k e^2}{r} \\$The total energy is the sum of kinetic and potential energy:$\\ E = K + U \\$Substituting the expressions for $K$ and $U: \\ E = \frac{k e^2}{2r} - \frac{k e^2}{r} \\$Simplifying the expression:$\\ E = -\frac{k e^2}{2r} \\$This confirms that the total energy $E$ is negative and equal to the negative of the kinetic energy.$\\$Now, let's find the ratio of kinetic energy to total energy:$\\ \frac{K}{E} = \frac{\frac{k e^2}{2r}}{-\frac{k e^2}{2r}} \\$Simplifying the ratio:$\\ \frac{K}{E} = -1 \\$Therefore, the ratio of kinetic energy to total energy is $1 : -1. \\$This corresponds to Option 2.