Physics · Atoms · NEET
The energy is negative because the electron is bound (trapped) by the nucleus. We choose the zero of energy at n = infinity, where the electron is just free and at rest. Any bound state has less energy than this free state, so it comes out negative. The formula E = -13.6/n^2 eV always gives a negative number for finite n. A more negative value means the electron is held more tightly. So -13.6 eV (n=1) is the most tightly bound, and -0.85 eV (n=4) is loosely bound.
Because E depends on 1/n^2, not on n. The gap between n=1 (-13.6 eV) and n=2 (-3.4 eV) is 10.2 eV, a huge jump. But n=3 is -1.51 eV and n=4 is -0.85 eV, only 0.66 eV apart. As n grows, 1/n^2 shrinks fast, so all the high levels pile up just below the 0 eV line. This crowding is why the emission lines of any series also crowd together near the series limit (shortest wavelength).
The 0 eV line is the ionisation level. It is the energy of a free electron that has just escaped the atom (at n = infinity) with no leftover kinetic energy. When the electron reaches this line, the atom is ionised. The energy needed to lift the electron from the ground state (-13.6 eV) up to this 0 eV line is the ionisation energy, 13.6 eV. Everything below 0 eV is a bound state; at or above 0 eV the electron is free.
They point to the same n, but they describe different things. An orbit (or shell) is a path or region in space where the electron can be, described by a radius r = 0.53 n^2 angstrom. An energy level is the fixed energy value the electron has when it is in that orbit, E = -13.6/n^2 eV. So orbit is about position and size, energy level is about energy. In the diagram we plot only the energy, so the vertical position of each line is its energy, not its radius.
Count states starting from the ground state. Ground state = n=1. First excited state = n=2. Second excited state = n=3. So the second excited state is n=3 with energy E = -13.6/3^2 = -13.6/9 = -1.51 eV. This exact wording is a common NEET trap, because students read second excited state as n=2. Always add: ground = n1, first excited = n2, second excited = n3.
A downward arrow (higher line to lower line) means emission: the atom gives out a photon of energy E_photon = E_high - E_low, and this energy is positive. An upward arrow means absorption: the atom takes in a photon to climb up. The length of the arrow tells you the photon energy, so a longer arrow means a larger energy and a shorter wavelength. Arrows ending at n=1 form the Lyman series (UV), ending at n=2 form the Balmer series (visible), ending at n=3 form the Paschen series (infrared).
The ground state energy of hydrogen atom is -13.6 eV. The energy needed to ionise a hydrogen atom from its second excited state will be:
The total energy of an electron in an atom in an orbit is -3.4 eV. Its kinetic and potential energies are, respectively:
Match List I (transitions in hydrogen) with List II (wavelengths in nm): (A) n2=3 to n1=2 (B) n2=4 to n1=2 (C) n2=5 to n1=2 (D) n2=6 to n1=2; wavelengths (I) 410.2 (II) 434.1 (III) 656.3 (IV) 486.1.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Using E = -13.6/n^2 eV: n=1 gives -13.6 eV (ground state), n=2 gives -3.4 eV, n=3 gives -1.51 eV, n=4 gives -0.85 eV. The top line at n = infinity is 0 eV, the free electron level.
The ground state (n=1) has the most negative energy, -13.6 eV, so it sits lowest on the vertical energy scale. It is the most stable and most tightly bound state. Electrons naturally fall to this level and release energy as light.
Each series is a group of downward arrows ending at the same lower level. Arrows ending at n=1 give the Lyman series (ultraviolet), at n=2 give the Balmer series (visible), at n=3 give the Paschen series (infrared), and so on. The diagram lets you see at a glance which transitions give which lines.
If the electron is in level n, the number of possible emission lines as it comes down is n(n-1)/2. For example, from n=4 you get 4(3)/2 = 6 lines. This counts every possible downward jump shown by arrows on the diagram.
Yes. For a hydrogen-like ion with atomic number Z, the levels become E = -13.6 Z^2 / n^2 eV. For He+ (Z=2) every level is 4 times more negative, so the ground state is -54.4 eV. The pattern of crowding near 0 eV stays the same, but the whole ladder is stretched downward.
