Question

A radioactive decay counter is switched on at t = 0. A b-active sample is present near the counter. The counter registers the number of b-particles emitted by the sample. The counter registers 1 × 10⁵b-particles at t = 36 sec and 1.11 × 10⁵b-particles at t = 108 sec. T_1/2 of this sample is

• A. 5.2 sec
• B. 10.8 sec
• C. 15.4 sec
• D. 20.6 sec

Answer 1

Answer: (B)

10.8 sec

Answer 2

N = N₀ e^–lt

Decay = N₀ – N

10⁵ = N₀ (1 – e^–36l)

1.11 × 10⁵ = N₀(1 – e^–108l)

Ž $\frac { 1 - \mathrm { e } ^ { - 108 \lambda } } { 1 - \mathrm { e } ^ { - 36 \lambda } }$ = 1.11

Ž e^–36l = 0.1 Ž $\lambda = \frac { \ln 10 } { 36 }$

$\mathrm { T } _ { 1 / 2 } = \frac { \ln 2 } { \lambda }$= $\frac { 36 \ln 2 } { \ln 10 }$ 10.8