Q.37. The ascending order of half-life for the radioactive isotopes, ¹²⁵I, ³H, ¹⁴C and ³²P, is:

(A) ¹⁴C < ¹²⁵I < ³H < ³²P

(B) ³²P < ³H < ¹²⁵I < ¹⁴C

(C) ¹⁴C < ³H < ³²P < ¹²⁵I

(D) ³²P < ¹²⁵I < ³H < ¹⁴C

Ascending Order of Half-Life of ¹²⁵I, ³H, ¹⁴C and ³²P

Correct Answer: (D)
³²P < ¹²⁵I < ³H < ¹⁴C

Half-lives of the given isotopes (approximate)

• ³²P (Phosphorus-32): 14.3 days
• ¹²⁵I (Iodine-125): about 59–60 days
• ³H (Tritium): 12.3 years
• ¹⁴C (Carbon-14): 5730 years

Arranging from shortest to longest half-life:
³²P < ¹²⁵I < ³H < ¹⁴C,
which corresponds to option (D).

Explanation of Each Option

Option (A): ¹⁴C < ¹²⁵I < ³H < ³²P

This option places ¹⁴C as having the shortest half-life and ³²P as the longest,
which is the reverse of reality. ¹⁴C actually has the longest half-life (thousands of years),
while ³²P has one of the shortest (about two weeks). Hence, this option is incorrect.

Option (B): ³²P < ³H < ¹²⁵I < ¹⁴C

This option correctly places ³²P as the shortest and ¹⁴C as the longest,
but it misorders ³H and ¹²⁵I. Since ¹²⁵I has a half-life of about
60 days and ³H has a half-life of 12.3 years, ¹²⁵I should come before
³H. Therefore, this option is incorrect.

Option (C): ¹⁴C < ³H < ³²P < ¹²⁵I

This option completely misorders the sequence by placing ¹⁴C as the shortest-lived isotope.
In reality, ¹⁴C is the longest-lived among the given isotopes, so this option is incorrect.

Option (D): ³²P < ¹²⁵I < ³H < ¹⁴C

³²P has the shortest half-life (~14.3 days), followed by ¹²⁵I (~59–60 days),
then ³H (12.3 years), and finally ¹⁴C (5730 years). This sequence correctly
represents the ascending order of half-life.

Exam Tip

Remember the time scale:
days (< ³²P) → months (< ¹²⁵I) → years (< ³H) → thousands of years (< ¹⁴C).
This makes it easy to recall the correct ascending order in exams.