Step-by-step Solution:

1. Analyze the initial substance: The question is about concentrated nitric acid ($HNO_3$). Pure concentrated nitric acid is a colorless fuming liquid.

2. Consider the effect of 'long standing': When nitric acid is left to stand for a long time, especially when exposed to light, it undergoes slow thermal or photochemical decomposition. This instability is a known chemical property of concentrated nitric acid.

3. Write the chemical equation for decomposition: The decomposition reaction of nitric acid is as follows: $4HNO_3(l) \longrightarrow 4NO_2(g) + O_2(g) + 2H_2O(l)$

4. Examine the products of the decomposition:

   • Nitrogen dioxide ($NO_2$): This is a reddish-brown gas.
   • Oxygen ($O_2$): This is a colorless gas.
   • Water ($H_2O$): This is a colorless liquid.

5. Relate the products to the observed color change: The question states that the nitric acid turns yellow-brown. Among the products, nitrogen dioxide ($NO_2$) is the colored species. The reddish-brown $NO_2$ gas produced during the decomposition dissolves in the remaining concentrated nitric acid, imparting a yellow-brown color to the solution. The intensity of the color depends on the concentration of the dissolved $NO_2$.

6. Evaluate the given options:

   • A: NO (Nitric oxide): This is a colorless gas. Its formation would not explain the yellow-brown color.
   • B: $NO_2$ (Nitrogen dioxide): This is a reddish-brown gas. Its dissolution in nitric acid correctly explains the observed yellow-brown coloration. This is the correct answer.
   • C: $N_2O$ (Nitrous oxide): This is a colorless gas, also known as laughing gas. It would not cause a color change.
   • D: $N_2O_4$ (Dinitrogen tetroxide): Nitrogen dioxide ($NO_2$) exists in equilibrium with its dimer, dinitrogen tetroxide ($N_2O_4$): $2NO_2 \rightleftharpoons N_2O_4$. While $N_2O_4$ is present, it is a colorless gas/liquid. The color of the mixture is due to the presence of the monomer, $NO_2$. Therefore, $NO_2$ is the direct cause of the color.

Conclusion:

The yellow-brown color that concentrated nitric acid develops upon long standing is due to the formation of nitrogen dioxide ($NO_2$) from its slow decomposition, which then dissolves in the acid.