GATE Half-Life PROBLRMS

GATE 2013
Q.16 If a radioactive isotope has a decay constant of 1.55 × 10-10 year-1, its half-life (in years) would be
(A) 4.57 × 109
(B) 4.47 × 109
(C) 4.57 × 1010
(D) 4.47 × 1010

GATE 2015
Q.20 The pair of curves that depicts the radioactive decay and growth of a parent-daughter pair in the following figure is (N – Number of nuclides, Time in multiples of half-life).

(A) P, Q
(C) P, S
(B) P, R
(D) S, Q

GATE 2016
Q.10 Which one of the following parent-daughter systems has the longest half life?
(A) 147Sm → 143Nd
(B) 40K → 40Ar
(C) 87Rb → 87Sr
(D) 187Os → 187Re

GATE 2016
Q.52 The fraction of a radioactive nuclide remaining after 10 half-lives is closest to
(A) 0.1
(B) 0.01
(C) 0.001
(D) 0.0001

GATE 2013
Q.16 If a radioactive isotope has a decay constant of 1.55 × 10-10 year-1, its half-life (in years) would be
(A) 4.57 × 109
(B) 4.47 × 109
(C) 4.57 × 1010
(D) 4.47 × 1010

GATE 2018
Q.80 The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is _______.

GATE 2019
Q.55 87Rb decays to 87Sr with a decay constant ?= 1.42 × 10-11 per year. If at the time of
formation, a system contains 8× 104 atoms of 87Rb and 103 atoms of 87Sr, the number of 87Sr atoms in this system at the end of 4 half-lives will be ________×103. Assume close system evolution for parent-daughter pair.

GATE 2019
Q.85 The abundance of 234U in secular equilibrium with its parent 238U will be ______×10-3 %. (Given Half-life (T1/2) of 238U and 234U are 4.467×109 y and 2.44×105 y, respectively, and abundance of 238U is 99.28%)(round off to 2 decimal places)