The figure that is not a direct manifestation of the quantum nature of atom is:

We need to determine which of the provided figures cannot be explained as a direct manifestation of the quantum nature of atoms.

Phenomena Guided by Quantum Nature:

The quantum nature of matter and radiation is fundamentally characterized by discrete energy levels, localized packet-like behaviors (photons), and deviations from classical continuous physical principles:

• Black-body Radiation Curve: The intensity vs. wavelength distribution cannot be justified using classical wave theory. Its accurate explanation relies strictly on Planck's Quantum Hypothesis, where energy is emitted or absorbed in discrete packets called quanta.
• Photoelectric Effect: The linear graph of the kinetic energy of photoelectrons versus the frequency of incident radiation exhibits a clear threshold behavior. This is directly validated by Einstein's photon model of light, demonstrating its quantized particle nature.
• Absorption/Emission Line Spectra: The presence of precise, distinct dark lines against a continuous wavelength background occurs because electrons transition exclusively between fixed, quantized electronic energy states within an atom.

Classical Manifestation (The Exception):

Let's evaluate the behavior of the internal energy of Argon ($$\text{Ar}$$) as a function of temperature:

• Argon is a monoatomic noble gas. According to the Classical Kinetic Theory of Gases and the law of equipartition of energy, its internal energy ($$\text{U}$$) is composed solely of continuous translational motion components:
$$U = \frac{3}{2}RT$$
• As the temperature increases, the internal energy scales up perfectly linearly and continuously, without involving quantized transitions or discrete quantum atomic configurations. Consequently, it represents a standard classical macroscopic thermodynamic relationship rather than a quantum phenomenon.

Conclusion:

Unlike the other options that strictly call for a quantum mechanical description, the linear progression of the internal energy of argon with temperature is fully explained by classical kinetic theory.

Answer: The option showing the graph of Internal energy of Ar vs Temperature (K).