Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# The Count Rate of Nuclear Radiation Coming from a Radiation Coming from a Radioactive Sample Containing 128i Varies with Time as Follows. - Physics

Sum

The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing 128I varies with time as follows.

 Time t (minute): 0 25 50 75 100 Ctount rate R (109 s−1): 30 16 8 3.8 2

(a) Plot In (R0/R) against t. (b) From the slope of the best straight line through the points, find the decay constant λ. (c) Calculate the half-life t1/2.

#### Solution

(a) For t = 0,

"In" (R_0/R) = "In" ((30 xx 10^9)/(30 xx 10^9)) = 0

For t = 25 s,

"In" (R_0/R_2) = "In" ((30 xx 10^9)/(16 xx 10^9)) = 0.63

For = 50 s,

"In" (R_0/R_3) = "In" ((30 xx 10^9)/(8 xx 10^9)) = 1.35

For t = 75 s,

"In" (R_0/R_4) = "In" ((30 xx 10^9)/(3.8 xx 10^9)) = 2.06

For t = 100 s,

"In" (R_0/R_5) = "In" ((30 xx 10^9)/(2 xx 10^9)) = 2.7

The required graph is shown below.

(b) Slope of the graph = 0.028
∴ Decay constant,  lambda = 0.028 "min"^-1

The half-life period (T_"1/2") is given by

T_"1/2" = 0.693/lambda

= 0.693/0.028 = 25  "min"

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 24 The Nucleus
Q 35 | Page 443
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