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First Order Reaction

A parent nucl...

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A parent nucleus $X$ is decaying into daughter nucleus $Y$ which in turn decays to $Z$ . The half-life of $X$ and $Y$ are $40000$ years and $20$ years respectively. In a certain sample, it is found that the number fo $Y$ nuclei in the sample is $X 4 \times 10^{20}$ , the number of $Y$ nuclei present in it is:

A

2 \times 10^{17}

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B

2 \times 10^{20}

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C

4 \times 10^{23}

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D

4 \times 10^{20}

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Q. A parent nucleus

X

is decaying into daughter nucleus

Y

which in turn decays to

Z

. The half lives of

X

Y

40000

20

years respectively. In a certain sample, it is found that the number of

Y

nuclei hardly changes with time. If the number of

X

nuclei in the sample is

4 \times 10^{20}

, the number of

Y

nuclei present in it is

Q. A sample contains two radioactive nuclei

x

y

with half-lives

2

1

hour respectively. The nucleus

x - d e c a y s

y

y - d e c a y s

into a stable nucleus

z

t = 0

the activities of the components in the same were equal. Find the ratio of the number of the active nuclei of

y

t = 1

hours to the number at

t = 0

.

Q. A radioactive nucleus

X

decays to a nucleus

Y

with a decay constant

λ_{x} = 0.1 s e c^{- 1}

Y

further decays to a stable nucleus

Z

with a decay constant

λ_{Y} = 1 / 30 s e c^{- 1}

. Initially, there are only

X

nuclei and their number is

N_{0} = 10^{20}

. Set up the rate equations for the populations of

X, Y

Z

. The population of the

Y

nucleus as a function of time is given by

N_{Y} (t) = {N_{0} λ_{X} / (λ_{X} - λ_{Y})} {e x p (- λ_{Y} t) - e x p (- λ_{X} t)}

. Find the time at which

N_{Y}

is maximum and determine the population

X

Z

at that instant.

4 \times 10^{23}

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

2.3 years

. The activity of the sample is

Q. The half-life of a radioactive isotope

X

20 years .

It decays into another element

Y

, which is stable. The two elements

X

Y

were found to be in the ratio

1 : 7

, in a sample of a given rock. The age of the rock is estimated to be,

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