Question

Energy of hydrogen atom in ground state is −13·6 eV. What will be the kinetic energy and the potential energy of the electron in the state?

Hint:

For hydrogen use \(K = -E\) and \(U = 2E\); the kinetic energy is positive and the potential energy is twice the total energy.

Answer 1

Step 1: Recall the energy relations in the Bohr model.
For an electron in a hydrogen atom, the total energy \(E\), kinetic energy \(K\), and potential energy \(U\) are related by
\[ K = -E \qquad\text{and}\qquad U = 2E \]
and also \(U = -2K\). These follow because the electron is bound by the attractive Coulomb force.

Step 2: Write the given data.
Total energy in the ground state: \(E = -13.6\ \text{eV}\).

Step 3: Find the kinetic energy.
\[ K = -E = -(-13.6) = +13.6\ \text{eV} \]

Step 4: Find the potential energy.
\[ U = 2E = 2 \times (-13.6) = -27.2\ \text{eV} \]

Step 5: Check.
\(K + U = 13.6 + (-27.2) = -13.6\ \text{eV} = E\), which is consistent.

\[\boxed{K = +13.6\ \text{eV},\qquad U = -27.2\ \text{eV}}\]