Question

For each value of $ 'l' $ the number of $ 'm' $ values are:
(A) $ 2l $
(B) $ 2l - 1 $
(C) $ 2l + 1 $
(D) $ n - 1 $

Answer 1

Hint: To answer this question you must be familiar with the concept of quantum numbers and the values that they take for a given orbital. There are four quantum numbers, namely, the principal quantum number, represented by $ n $ , orbital angular momentum or Azimuthal quantum number, represented by $ l $ , magnetic quantum number, represented by $ {m_l} $ and the spin quantum number represented by $ {m_s} $ .

Complete step by step solution
The magnetic quantum number describes the total number of the orbitals present in a given subshell. Its value depends on the azimuthal quantum number and it takes a total of $ \left( {2l + 1} \right) $ integral values from $ - l $ to $ + l $ .
The correct answer is C.

Note
The other three quantum numbers other than the magnetic quantum number are:
Principal quantum number describes the most probable distance between the nucleus of the atom and the electrons. Greater the value of the principal quantum number, greater is the distance between the electron and the nucleus. It denotes the shell in which the electron is present and takes natural number values. It also tells the energy of the shell.
The azimuthal quantum number describes the shape of the orbitals. Each value of this number gives a different shaped orbital. The value of the azimuthal quantum number depends on the principal quantum number and it takes only whole number values upto $ n - 1 $ .
The spin quantum number describes the direction in which the electron is spinning. It is independent of the values of the other quantum numbers. The spin quantum number takes only two values, either $ + 1/2 $ or $ - 1/2 $ .