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

Solution

Chemistry ma’am · 3 steps

Ask of each graph whether classical physics could explain it. Only the argon line passes that test.

1. What quantum means. A figure shows the quantum nature of atoms when energy comes in fixed packets: E = hν, or only certain allowed energy levels. If ordinary classical physics already explains the graph, it is not a quantum effect.

   Figure	What it shows	Explained by
   (a) Internal energy of Ar vs T	A straight line, U = 3/2RT per mole	Classical kinetic theory: argon atoms only move about
   (b) Absorption spectrum	Sharp lines that crowd together towards a limit	Quantum: only certain energy levels are allowed
   (c) Photoelectric effect	No electrons below a threshold frequency, then KE rises linearly with ν	Quantum: photons with E = hν
   (d) Black body radiation	Intensity peaks, and the peak shifts to shorter λ as T rises	Quantum: Planck's quantised energy

2. Why argon is classical. Argon is a monatomic gas, so its internal energy is only the kinetic energy of its atoms moving around. Between 300 K and 600 K no electron gets excited, so no energy levels show up and U just grows in proportion to T.
3. So. The internal energy plot of argon is the one that does not directly show the quantum nature of atoms. The answer is (a).

The idea to keep. Spectral lines, the photoelectric threshold and the black body curve are the three classic proofs of quantisation. A smooth straight line that kinetic theory already predicts is not.

Answer from the NTA final answer key. Solution by PrepWiser.