Physics · Atoms · NEET
The first excited state is n=2, not n=3. The counting starts from the ground state: n=1 is the ground state (zero excited), n=2 is the FIRST excited state, n=3 is the SECOND excited state, n=4 is the third excited state. So the excited-state number is always one less than n. This one-step gap is the single most tested trap in this topic.
Ground state energy is E1 = -13.6 eV. The formula is En = -13.6/n^2 eV. It is negative because the electron is bound to the nucleus. A bound electron has less energy than a free electron, and a free electron at rest far away is defined as 0 eV. So bound states are below zero, meaning energy must be supplied (added) to free the electron. The more negative the value, the more tightly bound and more stable the electron.
Use En = -13.6/n^2 eV and just plug in n. First excited state n=2: E2 = -13.6/4 = -3.4 eV. Second excited state n=3: E3 = -13.6/9 = -1.51 eV. Third excited state n=4: E4 = -13.6/16 = -0.85 eV. Notice the levels get closer together and closer to 0 as n increases - they crowd near the top of the energy ladder.
Ground state (n=1) is the natural, most stable, lowest-energy state where the electron normally stays; it needs no energy input. An excited state (n=2, 3, 4...) is a higher, temporary, less stable state reached only after the atom absorbs exactly the right energy. An excited electron falls back down within about 10^-8 seconds, emitting a photon. So ground state is permanent-by-default; excited states are short-lived.
This is the excitation energy for the n=1 to n=2 jump. Energy needed = E2 - E1 = (-3.4) - (-13.6) = +10.2 eV. The atom must absorb exactly 10.2 eV. Note this is different from the ionisation energy (13.6 eV needed to fully remove the electron from n=1).
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:
Let T1 and T2 be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to Bohr's model of an atom, the ratio T1 : T2 is:
The total energy of an electron in an atom in an orbit is -3.4 eV. Its kinetic and potential energies are, respectively:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Zero energy corresponds to a completely free electron at rest, infinitely far from the nucleus (n=infinity). A bound electron always has negative energy. As n increases the energy approaches 0 from below but only reaches 0 at the moment of ionisation.
The ground state (n=1, -13.6 eV) has the lowest (most negative) energy, which makes it the most stable. As you go to higher excited states the energy value rises toward 0, so those states are less stable.
Only about 10^-8 seconds (10 nanoseconds). The electron quickly falls back to a lower level and emits a photon whose energy equals the gap between the two levels.
No. 10.2 eV is the excitation energy for the n=1 to n=2 jump. The ionisation energy of hydrogen is 13.6 eV, which is the energy to remove the electron completely from the ground state to n=infinity.
The gaps shrink. The jump from n=1 to n=2 is 10.2 eV, but from n=2 to n=3 it is only about 1.89 eV. Higher levels crowd together near the 0 eV line.
