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Half life of radioactive material

4 10^{23} tritium atoms are contained in a vessel. The half l

Question

Hard

Solving time: 4 mins

$4 \times 1 0^{23}$ tritium atoms are contained in a vessel. The half life of decay of tritium nuclei is $12.3$ yrs. Find :
(a) the activity of the sample.
(b) the number of decays in the next 10 hours.
(c) the number of decays in the next $6.15$ yrs.

Views: 5,715 students

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

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Elijah Discussed

4 \times 1 0^{23}

tritium atoms are contained in a vessel. The half life of decay of tritium nuclei is

12.3

yrs. Find :
(a) the activity of the sample.
(b) the number of decays in the next 10 hours.
(c) the number of decays in the next

6.15

yrs.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Given

N = 4 \times 1 0^{23}

t_{\frac{1}{2}} = 12.3

years

Activity

= \frac{d N}{dt}

λ n = \frac{0.69}{t _{\frac{1}{2}}} N

= \frac{0.693}{12.3} \times 4 \times 1 0^{23}

dis

/

year

= \frac{0.693 \times 4 \times 1 0 ^{28}}{12.3 \times 3600 \times 24 \times 365} dis / sec

= 7.146 \times 1 0^{14}

dis / sec

(b)

\frac{dN}{dt} = 7.146 \times 1 0^{14}

No. of decays in next 10 hrs

= 7.146 \times 1 0^{14} \times 10 \times 3600

= 257.256 \times 1 0^{17} = 2.75 \times 1 0^{19}

(c)

N = N_{O} e^{- λ t} = 2.82 \times 1 0^{28}

=

No. of atoms remained

No. of atoms disintegrated

= (4 - 2.82) \times 1 0^{28} = 1.18 \times 1 0^{28}

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Question Text	$4 \times 1 0^{23}$ tritium atoms are contained in a vessel. The half life of decay of tritium nuclei is $12.3$ yrs. Find : (a) the activity of the sample. (b) the number of decays in the next 10 hours. (c) the number of decays in the next $6.15$ yrs.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	141

$4 \times 1 0^{23}$ tritium atoms are contained in a vessel. The half life of decay of tritium nuclei is $12.3$ yrs. Find :
(a) the activity of the sample.
(b) the number of decays in the next 10 hours.
(c) the number of decays in the next $6.15$ yrs.

Text solutionVerified

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4×1023 tritium atoms are contained in a vessel. The half life of decay of tritium nuclei is 12.3 yrs. Find :(a) the activity of the sample.(b) the number of decays in the next 10 hours. (c) the number of decays in the next 6.15 yrs.

Text solutionVerified

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$4 \times 1 0^{23}$ tritium atoms are contained in a vessel. The half life of decay of tritium nuclei is $12.3$ yrs. Find :
(a) the activity of the sample.
(b) the number of decays in the next 10 hours.
(c) the number of decays in the next $6.15$ yrs.