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Asked by Joseph Last Modified
Answer In the ground state of a hydrogen atom, the total energy is equal to the negative of the ground state energy, which is −13.6 eV−13.6eV. This total energy consists of the sum of the kinetic energy and the potential energy of the electron.
Given that the total energy is −13.6 eV−13.6eV, we can express this as the sum of the kinetic energy (KK) and the potential energy (VV) of the electron:
Total energy=K+VTotal energy=K+V
Since the electron is bound to the nucleus in the hydrogen atom, the total energy is negative, indicating a bound state.
Given that the total energy is −13.6 eV−13.6eV, and assuming the potential energy is negative (since it contributes to the binding of the electron), we can express the kinetic energy as:
K=Total energy−VK=Total energy−V
Substituting the given value of the total energy, we have:
K=−13.6 eV−VK=−13.6eV−V
Now, knowing that the potential energy is negative and contributes to the binding of the electron, and since the total energy is the sum of kinetic and potential energies, the potential energy (VV) is simply the negative of the total energy:
V=−13.6 eVV=−13.6eV
Substituting this value of potential energy into the expression for kinetic energy, we get:
K=−13.6 eV−(−13.6 eV)=0 eVK=−13.6eV−(−13.6eV)=0eV
So, in the ground state of the hydrogen atom, the kinetic energy of the electron is 0 eV0eV, and the potential energy is −13.6 eV−13.6eV.
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