Read the following passage and answer the questions.
A glass discharge tube is filled with hydrogen gas at low pressure. A high voltage is applied across the tube, and an electric current passes through the gas. The tube then glows. A spectrometer is used to study the light that comes out of the tube. In Bohr’s model, the electron of a hydrogen atom can stay only in certain allowed energy states, called stationary states. The energy of the electron in the \(n\)th state is \(E_n=-13.6/n^{2}\ \mathrm{eV}\), where \(n = 1, 2, 3, \ldots\) In the tube, fast-moving electrons collide with the hydrogen atoms. These collisions raise some atoms to states of higher energy. Such an excited atom does not stay in that state for long. It soon falls back to a lower state and gives out a photon.
Consider the following statements about the hydrogen atoms in the tube:
(A) An energy of 10.2 eV is needed to raise a hydrogen atom from its ground state to its first excited state.
(B) An electron with a total energy above 0 eV is free and can have any value of energy.
(C) At room temperature, most of the hydrogen atoms are in excited states.
(D) The energy of the atom is the largest when its electron is in the orbit closest to the nucleus.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (B) only
A bound electron has a negative energy. The value 0 eV belongs to \( n=\infty \), where the electron is just removed from the atom.
(A) An energy of 10.2 eV is needed to raise a hydrogen atom from its ground state to its first excited state. — True. The first excited state is \( n=2 \):
\( \begin{aligned} E_2-E_1 &= -3.40-(-13.6) \\ &= 10.2\ \mathrm{eV} \end{aligned} \)
(B) An electron with a total energy above 0 eV is free and can have any value of energy. — True. Above 0 eV the electron is not bound to the nucleus. Its energy is not quantised, so a continuum of states exists there.
(C) At room temperature, most of the hydrogen atoms are in excited states. — False. At room temperature most atoms are in the ground state. Collisions in the tube excite only some of them, and these soon fall back.
(D) The energy of the atom is the largest when its electron is in the orbit closest to the nucleus. — False. The orbit closest to the nucleus is \( n=1 \). Its energy, \( -13.6\ \mathrm{eV} \), is the least, being the largest negative value.
NCERT (2026-27):
Energy levels – “… It means that the energy required to excite an electron in hydrogen atom to its first excited state, is an energy equal to E2 – E1 = –3.40 eV – (–13.6) eV = 10.2 eV. …”
Energy levels – “An electron can have any total energy above E = 0 eV. In such situations the electron is free. …”
Energy levels – “At room temperature, most of the hydrogen atoms are in ground state. …”
Energy levels – “The energy of an atom is the least (largest negative value) when its electron is revolving in an orbit closest to the nucleus i.e., the one for which n = 1. …”