Final Answer:
The designation is determined by the azimuthal quantum number (l), and for 's', l is 0. Therefore, 's' corresponds to l = 0, making the correct answer 'a) s'.
Step-by-step explanation:
(1) The letter designation of an atomic orbital is given by the azimuthal quantum number (l). For the options provided:
- a) s corresponds to l = 0
- b) p corresponds to l = 1
- c) d corresponds to l = 2
- d) f corresponds to l = 3
(2) The azimuthal quantum number defines the shape of the orbital. It ranges from 0 to n-1, where n is the principal quantum number. In this case, since we are dealing with the letter designation 's', the azimuthal quantum number is 0.
(3) Therefore, the correct letter designation for an atomic orbital is determined by the value of the azimuthal quantum number. In the case of option 'a', which is 's', the azimuthal quantum number (l) is 0. Hence, the correct answer is 'a) s'.
In summary, the letter designation for an atomic orbital is based on the azimuthal quantum number, and 's' corresponds to l = 0.
Therefore, the correct answer to the given question is 'a) s'.