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A ${}^{7}{Li}$ target is bombarded with a proton beam current of magnitude $10^{- 4} A$ for an hour to produce ${}^{7}{Be}$ of activity $1.8 \times 10^{8}$ disintegrations per second. If we assume that one radioactive nucleus of beryllium is produced by bombarding $1000$ protons, then its half-life is close to

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Important Questions on Nuclear Physics

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

The half-life of a particle of mass

1.6 \times 10^{- 26} kg

6.9 s

and a stream of such particles is travelling with the

K . E .

of a particle being

0.05 eV

. The fraction of particles which will decay when they travel a distance of

1 m

is,

EASY

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

A radioactive nucleus

A

with a half-life

T

, decays into a nucleus

B

. At

t = 0

, there is no nucleus

B

. At some time

t

, the ratio of the number of

B

to that of

A

0.3

. Then,

t

is given by:

(Consider \log_{e} (x) = \log (x))

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Two species of radioactive atoms are mixed in equal number. The disintegration of the first species is

λ

and of the second is

\frac{λ}{3}

. After a long time the mixture will behave as a species with mean life of approximately

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Half-lives of two radioactive elements

A

and

B

are

20 minutes

and

40 minutes

, respectively. Initially, the samples have an equal number of nuclei. After

80 minutes

, the ratio of decayed numbers of

A

and

B

nuclei will be:

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

At a given instant, say

t = 0,

two radioactive substance

A

and

B

have equal activities. The ratio

\frac{R_{B}}{R_{A}}

of their activities after time

t

itself decays with time

t

e^{- 3 t} .

If the half-life of

A

l n 2,

the half-life of

B

is:

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

A piece of wood from a recently cut tree shows

20

decays per minute. A wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows

2

decays per minute. If the half-life of

C^{14}

5730 years

, then the age of the wooden piece placed in the museum is approximately
[This question was awarded a bonus and proper correction was made to avoid that]

EASY

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

A radioactive element has a rate of disintegration

10, 000

disintegrations per minute at a particular instant. After four minutes it becomes

2500

disintegrations per minute. The decay constant per minute is

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

A radio isotope ‘

X

’ with a half life

1.4 \times 10^{9}

years decays to ‘

Y

’ which is stable. A sample of the rock from a cave was found to contain ‘

X

’ and ‘

Y

’ in the ratio

1 : 7

. The age of the rock is

HARD

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Let

N_{β}

be the number of

β

particle emitted by

1 gram

{Na}^{24}

radioactive nuclei having a half life of

15 h

. In

7.5 h

, the number

N_{β}

is close to

[N_{A} = 6 .023 \times 10^{23} {mole}^{- 1}]

EASY

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

The half-life of a radioactive substance is

30 \min

. The time (in minutes) taken between

40 %

decay and

85 %

decay of the same radioactive substance is

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Two radioactive substances

A

and

B

have decay constants

5 λ

and

λ

respectively. At

t = 0

, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become

{(\frac{1}{e})}^{2}

will be

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At

t = 0

it was

1600

counts per second and

t = 8

seconds it was

100

counts per second. The count rate observed, as counts per second, at

t = 6

seconds is close to:

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Two radioactive materials

A

and

B

have decay constants

10 λ

and

λ

, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of

A

to that of

B

will be

\frac{1}{e}

after a time:

EASY

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Radioactive material

A

has decay constant

8 λ

and material

B

has decay constant

λ

. Initially they have the same number of nuclei. After what time, the ratio of number of nuclei of material

A

to that

B

will be

\frac{1}{e} ?

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

Half lives of two radioactive nuclei

A

and

B

are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

The activity of a radioactive sample falls from

700 s^{- 1}

500 s^{- 1}

30

minutes. Its half life is close to:

HARD

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

In a radioactive sample,

_{19}^{40} K

nuclei either decay into stable

_{20}^{40} C a

nuclei with decay constant

4.5 \times 10^{- 10}

per year or into stable

_{18}^{40} A r

nuclei with decay constant

0.5 \times 10^{- 10}

per year. Given that in this sample all the stable

_{20}^{40} C a

and

_{18}^{40} A r

nuclei are produced by the

_{19}^{40} K

nuclei only. In time

t \times 10^{9}

years, if the ratio of the sum of stable

_{20}^{40} C a

and

_{18}^{40} A r

nuclei to the radioactive

_{19}^{40} K

nuclei is

99,

the value of t will be : [Given

l n 10 = 2.3

]

HARD

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

At some instant, a radioactive sample

S_{1}

having an activity

5 μ Ci

has twice the number of nuclei as another sample

S_{2}

which has an activity of

10 μ Ci

. The ratio of half lives of

S_{1} a n d S_{2}

MEDIUM

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

In a radioactive decay chain, the initial nucleus is

_{90}^{232} Th

. At the end, there are

6

α

-particles and

4 β

-particles which are emitted. If the end nucleus is

_{Z}^{A} X, A

and

Z

are given by:

HARD

Physics>Modern Physics>Nuclear Physics>Radioactive Decay Law

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life

18

days inside the laboratory. Tests revealed that the radiation was

64

times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

A Li7 target is bombarded with a proton beam current of magnitude 10-4 A for an hour to produce Be7 of activity 1.8×108 disintegrations per second. If we assume that one radioactive nucleus of beryllium is produced by bombarding 1000 protons, then its half-life is close to

Important Questions on Nuclear Physics

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