The element whose salts cannot be detected by flame test is:
A) $Mg$
B) $Na$
C) $Cu$
D) $Sr$

Hint: In flame test a given compound is placed in the flame of a gas burner, then they give a characteristic colour that is visible to the naked eye because of the excitation and relaxation of the electrons in between energy levels. If the flame is unable to excite the electrons then the compound cannot be detected by flame test.

Complete step-by-step answer:
Flame test is an analytical procedure used to detect the presence of certain elements, primarily metal ions, based on each element's characteristic line emission spectrum due to excitation of gas. When the atoms of a gas or vapour are excited by heating applied from the flame the electrons present in the compound are able to move from their ground state to higher energy levels.

As they return to their ground state following clearly defined paths according to quantum probabilities, they emit photons of very specific energy. This energy corresponds to particular wavelengths of light and so produces particular colours of light. Each element has a fingerprint in terms of its line emission spectrum. Because each element has an exactly defined line spectrum, we can identify a given compound by the colour of flame they produce.

We know Beryllium being a second row element has small size and very high ionization enthalpy. Now, Magnesium has a diagonal relationship with Beryllium and hence are identical in their characteristics having small size and very high ionization enthalpy. The energy of the flame is not sufficient to excite the electrons to higher energy levels. So magnesium does not give a flame test while Copper produces a blue flame, Sodium produces a yellow flame and Strontium produces a red flame.

Hence the correct answer is (i) $Mg$.

Note: For this question you must have proper knowledge of both the principle behind flame test used for detection of a compound and the position of the different elements present in the periodic table. If you don’t know one of them then solving the question will be difficult