CBSE Class 12 Physics (2026–27)
Chapter 12: Atoms
20 Important Questions and Answers
Q1. What were the main postulates of Rutherford’s atomic model?
Answer:
Rutherford proposed that an atom consists of a tiny, dense, positively charged nucleus located at its center. Almost the entire mass of the atom is concentrated in this nucleus. Electrons revolve around the nucleus in circular paths due to electrostatic attraction. Most of the atom’s volume is empty space, which explains why most alpha particles pass through a thin metal foil without deflection. However, a few particles are deflected through large angles due to the strong repulsive force from the nucleus. Although Rutherford’s model explained the scattering experiment successfully, it failed to explain the stability of atoms and the discrete line spectra observed in atomic emissions.
Q2. Why was Rutherford’s atomic model considered unstable?
Answer:
According to classical electromagnetic theory, any charged particle moving in a circular path continuously emits electromagnetic radiation. Since electrons revolve around the nucleus, they should lose energy continuously. As a result, their orbital radius would gradually decrease, causing them to spiral into the nucleus. This would lead to the collapse of the atom within a very short time. However, atoms are stable in nature and do not collapse. Rutherford’s model could not explain this stability. It also failed to account for the discrete spectral lines emitted by atoms. These shortcomings led to the development of Bohr’s atomic model.
Q3. State Bohr’s first and second postulates of the hydrogen atom.
Answer:
Bohr’s first postulate states that electrons revolve around the nucleus only in certain stable circular orbits called stationary states without radiating energy. In these orbits, the total energy of the electron remains constant. The second postulate states that only those orbits are allowed for which the angular momentum of the electron is quantized. Mathematically, it is given by (mvr = \frac{nh}{2\pi}), where (n) is the principal quantum number. These postulates successfully explained the stability of atoms and the observed line spectrum of hydrogen.
Q4. What is meant by stationary orbits in Bohr’s theory?
Answer:
Stationary orbits are the special circular paths around the nucleus in which electrons revolve without losing energy. According to Bohr, electrons in these orbits neither emit nor absorb electromagnetic radiation despite being accelerated. Each stationary orbit has a definite energy associated with it. Electrons remain stable in these energy levels until they gain or lose energy. When an electron jumps from one stationary orbit to another, radiation is emitted or absorbed. The concept of stationary orbits successfully explained atomic stability and the existence of discrete energy levels in hydrogen atoms.
Q5. State Bohr’s frequency condition.
Answer:
Bohr’s frequency condition explains the emission or absorption of radiation during electronic transitions between energy levels. According to this condition, when an electron jumps from a higher energy orbit to a lower energy orbit, a photon is emitted. Conversely, when it moves to a higher orbit, a photon is absorbed. The frequency of the emitted or absorbed radiation is given by:
[h\nu = E_2 – E_1]
where (h) is Planck’s constant, (\nu) is the frequency, and (E_1) and (E_2) are the energies of the two states. This condition successfully explained the line spectra of hydrogen.
Q6. What is the radius of the first Bohr orbit? Explain its significance.
Answer:
The radius of the first Bohr orbit, known as the Bohr radius, is:
[a_0 = 0.529 \times 10^{-10}, m]
It represents the smallest stable orbit of an electron in a hydrogen atom. The Bohr radius serves as a fundamental unit for measuring atomic dimensions. The radius of higher orbits is proportional to the square of the principal quantum number ((r_n = n^2a_0)). This concept helped scientists estimate atomic sizes and provided quantitative support to Bohr’s model. The Bohr radius remains an important constant in atomic physics and quantum mechanics.
Q7. Define the principal quantum number and its significance.
Answer:
The principal quantum number, represented by (n), specifies the energy level or shell occupied by an electron in an atom. Its values are positive integers such as 1, 2, 3, and so on. A larger value of (n) corresponds to a higher energy level and a larger orbital radius. The energy and radius of Bohr orbits depend directly on the principal quantum number. Electrons in higher energy levels are less tightly bound to the nucleus. The principal quantum number thus determines the size, energy, and position of an electron within an atom.
Q8. What is the expression for the energy of an electron in the nth orbit?
Answer:
According to Bohr’s theory, the total energy of an electron in the nth orbit of a hydrogen atom is given by:
[E_n = -\frac{13.6}{n^2}, eV]
The negative sign indicates that the electron is bound to the nucleus. As the value of (n) increases, the energy becomes less negative, indicating that the electron is farther from the nucleus. At (n = \infty), the energy becomes zero, meaning the electron is completely free from the atom. This expression successfully explained the discrete energy levels observed in hydrogen spectra.
Q9. What is excitation energy?
Answer:
Excitation energy is the minimum amount of energy required to raise an electron from the ground state to a higher energy state within an atom. For hydrogen, the ground-state energy is –13.6 eV. To excite the electron to the first excited state ((n = 2)), the required energy is:
[E = -3.4 – (-13.6) = 10.2, eV]
When this energy is supplied, the electron moves to a higher orbit. The atom becomes excited but remains neutral. Excitation energy is important in understanding atomic spectra and electronic transitions.
Q10. What is ionization energy of hydrogen atom?
Answer:
Ionization energy is the minimum energy required to remove an electron completely from an atom in its ground state. For a hydrogen atom, the electron in the ground state has an energy of –13.6 eV. To free the electron completely, 13.6 eV of energy must be supplied. This process is called ionization. After ionization, the electron becomes free and the hydrogen atom turns into a positively charged ion. Ionization energy is a measure of how strongly an electron is bound to the nucleus and is an important atomic property.
Q11. What is the ground state and excited state of an atom?
Answer:
The ground state is the lowest energy state of an atom in which the electron occupies the nearest possible orbit to the nucleus. For hydrogen, this corresponds to (n = 1). When an electron absorbs energy and moves to a higher orbit ((n > 1)), the atom is said to be in an excited state. Excited states are unstable and have higher energy than the ground state. After a short time, the electron returns to a lower energy level by emitting radiation. These transitions produce characteristic spectral lines.
Q12. What are spectral lines?
Answer:
Spectral lines are distinct bright or dark lines observed in the spectrum of light emitted or absorbed by atoms. They arise due to electronic transitions between different energy levels. When an electron falls from a higher energy level to a lower one, it emits radiation of a specific wavelength, producing an emission line. Conversely, absorption lines are produced when electrons absorb energy and move to higher levels. Since each element has unique energy levels, its spectral pattern is also unique. Spectral lines are therefore used to identify elements.
Q13. State the Rydberg formula for hydrogen spectrum.
Answer:
The wavelengths of spectral lines in hydrogen are given by the Rydberg formula:
[\frac{1}{\lambda}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)]
where (R = 1.097 \times 10^7, m^{-1}) is the Rydberg constant, (n_1) is the lower energy level, and (n_2) is the higher energy level. The formula successfully explains all spectral series of hydrogen such as Lyman, Balmer, and Paschen series. It was later theoretically justified using Bohr’s atomic model. The formula accurately predicts the wavelengths of emitted or absorbed radiation.
Q14. What is the Lyman series?
Answer:
The Lyman series consists of spectral lines produced when electrons in hydrogen atoms transition from higher energy levels ((n = 2, 3, 4,) etc.) to the first energy level ((n = 1)). These transitions emit ultraviolet radiation. The shortest wavelength corresponds to the series limit when (n = \infty) to (n = 1). The Lyman series was one of the first hydrogen spectral series discovered and played an important role in understanding atomic structure. It provides strong evidence for quantized energy levels in atoms.
Q15. What is the Balmer series?
Answer:
The Balmer series consists of spectral lines produced when electrons fall from higher energy levels ((n = 3, 4, 5,) etc.) to the second energy level ((n = 2)) in hydrogen atoms. These spectral lines lie mainly in the visible region of the electromagnetic spectrum. The Balmer series was discovered experimentally before Bohr’s theory and was later explained using quantized energy levels. The visible nature of these lines makes them particularly important in spectroscopy and astronomical observations. They provide direct evidence for atomic energy quantization.
Q16. What is the Paschen series?
Answer:
The Paschen series is formed when electrons in hydrogen atoms transition from higher energy levels ((n = 4, 5, 6,) etc.) to the third energy level ((n = 3)). The emitted radiation lies in the infrared region of the electromagnetic spectrum. This series is not visible to the human eye but can be detected using infrared instruments. The Paschen series, along with other hydrogen spectral series, confirms the existence of discrete energy levels in atoms. It is important in astrophysics and infrared spectroscopy.
Q17. How did Bohr’s theory explain the hydrogen spectrum?
Answer:
Bohr explained the hydrogen spectrum by proposing that electrons occupy fixed energy levels around the nucleus. An electron can move between these levels only by absorbing or emitting a photon whose energy equals the difference between the two levels. Since only specific energy levels are allowed, only certain photon frequencies can be emitted or absorbed. This results in discrete spectral lines rather than a continuous spectrum. Bohr’s calculations accurately matched the observed wavelengths of hydrogen spectral lines, providing strong support for the quantized nature of atomic energy.
Q18. Mention two successes of Bohr’s atomic model.
Answer:
Bohr’s atomic model successfully explained the stability of atoms by introducing stationary orbits in which electrons do not radiate energy. It also explained the line spectrum of hydrogen by assuming quantized energy levels and electronic transitions between them. The model accurately predicted the wavelengths of hydrogen spectral lines and provided theoretical justification for the Rydberg formula. Additionally, it introduced the concept of quantized angular momentum, which became a foundation for quantum theory. These achievements made Bohr’s model a major milestone in atomic physics.
Q19. Mention two limitations of Bohr’s atomic model.
Answer:
Bohr’s model could successfully explain only hydrogen and hydrogen-like atoms but failed for multi-electron atoms. It could not account for the fine structure and relative intensities of spectral lines. The model also failed to explain the Zeeman effect and Stark effect, where spectral lines split under magnetic and electric fields. Furthermore, it was inconsistent with the wave nature of electrons proposed later by quantum mechanics. Due to these limitations, Bohr’s model was eventually replaced by the more comprehensive quantum mechanical model of the atom.
Q20. What is meant by hydrogen-like atoms?
Answer:
Hydrogen-like atoms are atoms or ions that contain only one electron orbiting the nucleus. Examples include He⁺, Li²⁺, and Be³⁺. Since they possess only one electron, their atomic structure is similar to that of hydrogen. Bohr’s theory can be successfully applied to these systems with slight modifications involving the nuclear charge (Z). The energy levels and spectral lines of hydrogen-like atoms depend on (Z^2). These atoms are important for testing atomic theories and studying fundamental atomic interactions.