Question

How can I calculate the ground state energy?

Answer 1

Hint: from the given ground state energy, we can calculate the kinetic energy by using $KE=-E$, where KE is the kinetic energy and E is the ground state energy. And the potential energy will be given by using $PE=2\times KE$ where PE is the potential energy and KE is the kinetic energy

Complete step by step solution:
Here we will take an example of hydrogen and try to calculate ground state energy.
The ground state of a quantum- mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. The kinetic energy of the electron is given as: $KE=-E$
Where, KE is the kinetic energy and E is the ground state energy. Kinetic Energy: The Kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
$\therefore KE=-(-13.67eV)$
Thus, $ KE=+13.67eV$ The potential energy of the electron is given as: $PE=-2\times KE$
Where PE is the potential energy and E is the ground state energy. Potential Energy: Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
\[PE=-2\times 13.67eV\text{ }\]
Thus, \[\therefore PE=-27.2eV\]
In short, in order to find ground state energy, we first need to find $KE$ and $PE$.

Note: The ground state energy is the total energy. \[E=\text{ }T+V\] where T and V are kinetic and potential energy of the system. Therefore adding the above values that is $13.67+(-27.2)$ gives the $-13.67eV$ which is the ground state energy (E).