In the decay sequence: U 92 238 → - x 1 Th 90 234 → - x 2 Pa 91 234 → - x 3 Z 234 → - x 4 Th 90 234 x 1 , x 2 , x 3 and x 4 are the particles/ radiation emitted by the respective isotopes. The correct option(s) is/are:

x 1 will deflect towards the negatively charged plate.

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$C^{14}$ has a half life of $5730$ years and its abundance in the atmosphere is $1$ in $10^{12}$ carbon atoms. A fresh sample of $0.001$ mole of ${CO}_{2}$ collected from the atmosphere records a decay of $1700 C^{14}$ atoms over a week. A large piece of old wood is burnt and $0.001$ mole of ${CO}_{2}$ collected from it records a decay of $430 C^{14}$ atoms over a week. Then the age of the wood is close to

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Important Questions on Structure of Atoms and Nuclei

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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]

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

In the decay sequence:

${}_{92}^{238}U \overset{- x_{1}}{\to} {}_{90}^{234}{Th} \overset{- x_{2}}{\to} {}_{91}^{234}{Pa} \overset{- x_{3}}{\to} {}^{234}Z \overset{- x_{4}}{\to} {}_{90}^{234}{Th}$

$x_{1}, x_{2}, x_{3}$ and $x_{4}$ are the particles/ radiation emitted by the respective isotopes. The correct option(s) is/are:

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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

]

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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:

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

The variation of decay rate with number of active nuclei is correctly shown in graph

A Question Image

B Question Image

C Question Image

D Question Image

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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,

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

A radioactive nucleus decays by two different processes. The half-life for the first process is

10 s

and that for the second is

100 s

. The effective half-life of the nucleus is close to:

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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:

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

Some amount of a radioactive substance (half-life

= 10

days ) is spread inside a room and consequently, the level of radiation becomes

50

times the permissible level for normal occupancy of the room. After how many days will the room be safe for occupation?

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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:

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

A radioactive sample of half life

23.1 days

is disintegrating continuously. The percentage decay of the sample between the

15^{th}

and

16^{th}

day will be [Take,

e^{0.03} = 1.03

]

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

Two radioactive materials

X_{1}

and

X_{2}

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

X_{1}

to that of

X_{2}

will be

\frac{1}{e}

after a time

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

A hypothetical radioactive element has a half-life of

20

years. The time it takes for

80 %

of the substance to decay is

(\ln 5 = 1.6, \ln 2 = 0.7)

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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} ?

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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}]

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Physics>Modern Physics>Structure of Atoms and Nuclei>Radioactivity

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:

Important Questions on Structure of Atoms and Nuclei

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