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

# The Decay Constant of 197 80 Hg (Electron Capture to 197 79 Au) is 1.8 × 10−4 S−1. (A) What is the Half-life? (B) What is the Average-life? (C) How Much Time Will It Take to Convert 25% - Physics

#### Question

The decay constant of ""_80^197Hg (electron capture to ""_79^197Au) is 1.8 × 10−4 S−1. (a) What is the half-life? (b) What is the average-life? (c) How much time will it take to convert 25% of this isotope of mercury into gold?

#### Solution

Given :-

Decay Constant of ""_80^197"Hg" , lambda = 1.8 xx 10^-4 "s"^-1

(a)

Half-life, T_"1/2" = 0.693/lambda

⇒ T_"1/2" = 0.693/(1.8 xx 10^-4)

= 3850 s=64 minutes

(b)

Average life, T_(av) = T_"1/2"/0.693

= 64/0.693

= 92 minutes

(c)

Number of active nuclei of mercury at t = 0 = N0 = 100

Active nuclei of mercury left after conversion of 25% isotope of mercury into gold = N =  75

Now , N/N_0 = e^(-lambda t)

Here,

N = Number of inactive nuclei
N_0 = Number of nuclei at t = 0
lambda = Disintegration constant

On substituting the values, we get

75/100 = e^(-lambdat)

⇒ 0.75 = e^(-lambda x)

⇒ "In"  0.75 = - lambda t

⇒ t = ("In" 0.75)/-0.00018

= 1600 s

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [1]

Solution The Decay Constant of 197 80 Hg (Electron Capture to 197 79 Au) is 1.8 × 10−4 S−1. (A) What is the Half-life? (B) What is the Average-life? (C) How Much Time Will It Take to Convert 25% Concept: Radioactivity - Law of Radioactive Decay.
S