The total energy of an electron in \( n^{th} \) orbit of the hydrogen atom can be expressed as \( E_{n} = -\displaystyle\frac{13.6Z^{2}}{n^{2}}\,eV \). The negative sign indicates:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Electrons are bound to the nucleus.
In the Bohr model the zero of energy is taken for the electron at rest infinitely far from the nucleus, i.e. a free electron. A negative total energy means that energy (the ionisation energy) must be supplied to free the electron.
Option (1) Electrons are free to move. — Incorrect. A free electron has zero or positive total energy; a negative energy means the opposite.
Option (2) The kinetic energy of the electron is equal to the potential energy of the electron. — Incorrect. In a Bohr orbit \( K = +13.6Z^{2}/n^{2}\,\mathrm{eV} \) and \( U = -2K \), so \( K = -U/2 \); the two are not equal.
Option (3) Electrons are bound to the nucleus. — Correct. The negative sign shows that the electron is in a bound state, held by the attraction of the nucleus.
Option (4) The atom is radiating energy. — Incorrect. In a stationary orbit the electron does not radiate (Bohr’s postulate); energy is radiated only in a transition between orbits.
NCERT (2026-27):
Bohr Model of the Hydrogen Atom – “… The negative sign of the total energy of an electron moving in an orbit means that the electron is bound with the nucleus. Energy will thus be required to remove the electron from the hydrogen atom to a distance infinitely far away from its nucleus (or proton in hydrogen atom).”