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.

HARD

Earn 100

The ratio of the components in a mixture, which consists of two elements, is to be determined. The atomic number of the elements are big, their atomic mass numbers are the same and the amount of the sample is only $58 mg$ . We know that both elements undergo $β$ decay when they are bombarded by neutrons. They behave similarly when absorbing neutrons. The half-life of element $A$ is half an hour and the half-life of element $B$ is an hour. Right after the neutron irradiation the $β$ emission is measured. At this time $80$ particles are measured in $2$ seconds, and after an hour only $29$ particles are measured during $2$ seconds. Determine the mass of the element $A$ (in $mg$ ) in the sample. Assume that spontaneous decay statistical law is obeyed by nuclei of both the elements.

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Important Questions on Atoms and Nuclei

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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]

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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,

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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:

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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?

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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:

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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>Atoms and Nuclei>Law of Radioactive Decay

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}]

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Law of Radioactive Decay

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 Atoms and Nuclei

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