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**Introductory Exercise 31.1**

**Ques 1: Activity of a radioactive substance decreases from 8000 8q to 1000 Bq in 9 days. What is the half life and average life of the radioactive substance?Sol:**

âˆ´ n = 3 = number of half lives There half lives are equivalent to 9 days. Hence one half life is 3 days.

t

Sol:

â‡’

where,

N = N

Find N

and N

Number of nuclei decayed in given time= N

(a) Find the decay constant and half life

(b) How many atoms of the isotope were contained in the freshly prepared sample?

(c) What is the sample's activity 30.0 h after it is prepared?

Sol:

R

R = 8 mci

t = 4.0 h Find Î».

(b) R0 =Î»N

Find.

(c) Find R = R

Sol:

6.0 Ã— 10

âˆ´ Î» = 6.0 Ã— 10

Sol:

n

= 200/50 = 4

n

= 200/100 = 2

**Introductory Exercise 31.2**

**Ques 1: (a) How much mass is lost per day by a nuclear reactor operated at a 10 ^{9} watt power level?**

Sol:

âˆ´

(b) Number of fissions required per second

= 3.125 Ã— 10

Given

Sol:

= (238.050784) - (234.043593 + 4.002602) = 4.589 Ã— 10

Energy released = Î”m Ã— 931.48 MeV = 4.27 MeV

**ExercisesFor JEE Main**

**Subjective QuestionsRadioactivity**

R = 2700 per minute, R

Find Î».

Sol:

6 Ã— 10

Î»= 6 Ã— 10

= 1155 s= 19.25 min

Sol:

= 7.14 Ã— 10^{19}^{}**Ques 4: The half-life of gainst alpha decay is 4.5 Ã— 10 ^{9} year. How much disintegration per second occurs in 1 g of ?Sol:**

= 1.23 x 10

âˆ´ Î» = 0.1 day

Probability of decay

= 1 â€“ e

Sol:

N

From Eqs. (i) and (ii), we get t = 1.88 Ã— 10

Sol:

Pb+ 10 protons + 20 neutrons

Are both the reactions possible?

Sol:

So this reaction is possible.

(b) 82 + 16 - 6 = 92, 206 + 32 = 238

But antineutrino is also emitted with Î²

m

Give your answer in units of MeV. [Remember 1 u = 931.5 Me V/c

Sol:

= (7 Ã— 1.00783 + 7 Ã— 1.00867-14.00307) 931.5 = 104.72 MeV

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