Physics · Atoms · NEET
Both are correct, they are just opposite signs. Total energy E_n = -13.6 Z^2/n^2 eV is negative because the electron is bound (trapped) near the nucleus. Binding energy is the ENERGY YOU MUST ADD to free it, so it is the positive number: BE = -E_n = +13.6 Z^2/n^2 eV. In the ground state, E_1 = -13.6 eV, so BE = +13.6 eV. Rule: binding energy is always reported as a positive value equal to |E_n|.
For hydrogen in the GROUND STATE they are numerically equal: 13.6 eV. Ionisation energy means energy to remove the electron starting from the ground state (n = 1). Binding energy can be stated for ANY level: it is the energy to free the electron from whatever level it currently sits in. So the binding energy of the n = 2 state is 3.4 eV, which is also the energy to ionise a hydrogen atom that is in n = 2. NCERT: 'The minimum energy required to free the electron from the ground state of hydrogen is 13.6 eV. It is called the ionisation energy.'
First excited state is n = 2. BE = 13.6/n^2 = 13.6/4 = 3.4 eV. The electron is held more loosely in higher orbits, so binding energy drops as n grows. Second excited state (n = 3): BE = 13.6/9 = 1.51 eV.
Multiply by Z^2. BE = 13.6 Z^2/n^2 eV. For He+ (Z = 2) ground state: 13.6 x 4 = 54.4 eV, so its electron is held four times more tightly than hydrogen. This links directly to the next topic, Bohr model for hydrogen-like ions.
In a Bohr orbit KE = +13.6 Z^2/n^2 eV and total energy E_n = -13.6 Z^2/n^2 eV, so KE = -E_n = BE. That is why binding energy, kinetic energy, and |total energy| all share the same number 13.6/n^2 eV. The potential energy is twice the total energy (PE = -27.2 eV in ground state).
The ground state energy of hydrogen atom is -13.6 eV. The energy needed to ionize hydrogen atom from its second excited state will be:
The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is the energy required to remove the electron completely from the atom. For the ground state (n = 1) of hydrogen it is 13.6 eV. In general BE = +13.6 Z^2/n^2 eV, always a positive value equal to the magnitude of the total energy of that level.
BE = +13.6 Z^2/n^2 eV, where Z is the atomic number and n is the principal quantum number. It equals -E_n, the negative of the total energy of the orbit.
Because the ground-state total energy of the hydrogen electron from Bohr's model is E_1 = -13.6 eV. Binding energy is the positive of this, so 13.6 eV. This matches the measured ionisation energy of hydrogen, confirming Bohr's model.
In a Bohr orbit KE = +13.6 Z^2/n^2 eV, PE = -27.2 Z^2/n^2 eV, and total energy E = -13.6 Z^2/n^2 eV. Binding energy = -E = KE. So numerically BE equals the kinetic energy, and PE is twice the total energy.
It decreases as n increases, because BE = 13.6/n^2 eV. Electrons in outer orbits are held more loosely: n = 1 gives 13.6 eV, n = 2 gives 3.4 eV, n = 3 gives 1.51 eV.
