To determine which phosphorus oxoacid can create a silver mirror from \(AgNO_3\) solution, we need to understand the silver mirror test, commonly known as Tollens' test. This test is used to detect the presence of an aldehyde group, as they can reduce silver ions to metallic silver.
The relevant phosphorus oxoacids in this question are:
In the silver mirror test, reducing agents can reduce \(Ag^+\) ions from \(AgNO_3\) to metallic silver, producing a visible mirror-like silver coating on the test tube. This reaction typically takes place with compounds containing the aldehyde group or substances with a relatively strong reducing power.
Let's analyze the reducing capabilities of these acids:
Given these considerations, the acid that can produce a silver mirror from \(AgNO_3\) is Hypophosphorous acid \((H_4P_2O_5)\). This is because it is known to possess sufficient reducing properties to convert silver ions into a metallic silver mirror.
Thus, the correct answer is \(H_4P_2O_5\), which is Hypophosphorous acid.