Answer
(a) $ -CI\gt -OH\gt -CH_{3} \gt -H $
(b) $-CH_{2}OH\gt -CH=CH_{2} \gt-CH_{2}CH_{3}\gt -CH_{3}$
(c) $-CO_{2}H\gt -CH_{2}OH\gt -C≡N\gt -CH_{2}NH_{2}$
(d) $-CH_{2}OCH_{3} \gt -C≡N \gt -C≡CH \gt-CH_{2}CH_{3}$
Work Step by Step
According to the sequence rules:
1. The number with higher atomic number has a higher priority over the atom with a lower atomic number.
2. If Rule 1 is not applicable (atoms have equal atomic numbers), look at the next atom successively until the decision can be made.
3. Multiple-bonded atoms are considered equal to the single bonded atoms of the same number.
Thus,
(a) $ -CI\gt -OH\gt -CH_{3} \gt -H $
Cl atom has the highest atomic number, followed by O, C and H.
(b) $-CH_{2}OH\gt -CH=CH_{2} \gt-CH_{2}CH_{3}\gt -CH_{3}$
The C atom in $-CH_{2}OH$ is bonded to one O atom and 2 H atoms (OHH), the C atom in $-CH=CH_{2}$ is bonded to 2 C atoms and one H atom (CCH) (according to rule 3).
The C atom in $-CH_{2}CH_{3}$ is bonded to one C and 2 H atoms (CHH) and the C atom in $-CH_{3}$ is bonded to 3 H atoms (HHH). So, the highest priority is given to the atom with the highest atomic number, i.e. O, then C, followed by H. Note that $-CH=CH_{2}$ gets a higher priority over $-CH_{2}CH_{3}$ as it has 2 C atoms bonded to it as opposed to one C atom in $-CH_{2}CH_{3}$.
(c) $-CO_{2}H\gt -CH_{2}OH\gt -C≡N\gt -CH_{2}NH_{2}$
The atom with a higher atomic number gets a higher priority, i.e. $O\gt N\gt C\gt H$ and thus, in $-CO_{2}H$, the C atom is bonded to 2 O atoms and one H atom (OOH); in $-CH_{2}OH$, the C atom is bonded to 2 H atoms and one O atom (OHH); in $-C≡N$, the C is bonded to 3 N atoms, (NNN); in $-CH_{2}NH_{2}$ the C atom is bonded to one N and 2 H atoms (NHH). since the priority order is $O>N>C>H$, the sequence order is $-CO_{2}H\gt -CH_{2}OH\gt -C≡N\gt -CH_{2}NH_{2}$.
(d)$-CH_{2}OCH_{3} \gt -C≡N \gt -C≡CH \gt-CH_{2}CH_{3}$
The C in $-CH_{2}OCH_{3}$ is bonded to one O and 2 H atoms (OHH); in $-C≡N$, the C is bonded to 3 N atoms (NNN); in $-C≡CH$, the C is bonded to 3 C atoms (CCC) and in $-CH_{2}CH_{3}$, the C atom is bonded to one c and 2 H atoms (CHH). the priority order is $ O>N>C>H and hence the arrangement.
