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The element curium $_{96}^{248} C m$ has a mean life of 10¹³ second. Its primary decay modes are spontaneous fission and α - decay, the former with a probability of 8% and the latter with a probability of 92%. Each fission releases 200 MeV of energy. The masses involved in decay are as follows:

$_{96}^{248} C m = 248.072220 u,_{2}^{4} He = 4.002603 u and_{94}^{244} Pu = 244.064100 u$ .

Calculate the power output from a sample of 10²⁰ Cm atoms. Given: 1u = 931 MeV/c².

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Important Questions on Nuclei

EASY

Physics>Modern Physics>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

HARD

Physics>Modern Physics>Nuclei>Radioactivity

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>Nuclei>Radioactivity

The beta particles of a radioactive metal originate from-

MEDIUM

Physics>Modern Physics>Nuclei>Radioactivity

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>Nuclei>Radioactivity

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:

EASY

Physics>Modern Physics>Nuclei>Radioactivity

A nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If

M (A, Z)

denotes the mass of a single neutral atom of an element with mass number A and atomic number Z, then the minimal condition that the

β

decay,

X_{Z}^{A} \to Y_{Z + 1}^{A} + β^{-} + \bar{v_{e}}

, will occur is (

m_{e}

denotes the mass of the

β

particle and the neutrino mass

m_{v}

can be neglected):

EASY

Physics>Modern Physics>Nuclei>Radioactivity

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>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]

EASY

Physics>Modern Physics>Nuclei>Radioactivity

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

HARD

Physics>Modern Physics>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}]

MEDIUM

Physics>Modern Physics>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,

MEDIUM

Physics>Modern Physics>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:

EASY

Physics>Modern Physics>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} ?

EASY

Physics>Modern Physics>Nuclei>Radioactivity

A decay chain of the nucleus

{}_{92}^{238}U

involves eight

α

-decays and six

β

-decays. The final nucleus at the end of the process will be

HARD

Physics>Modern Physics>Nuclei>Radioactivity

Carbon $- 11$ decays to boron $- 11$ according to the following formula: ${}_{6}^{11}C \to {}_{5}^{11}B + e^{+} + v_{e} + 0.96 MeV$ .
Assume that positrons $(e^{+})$ produced in the decay combines with free electrons in the atmosphere and annihilate each other almost immediately. Also, assume that the neutrinos $(v_{e})$ are massless and do not interact with the environment. At $t = 0$ , we have $1 μg$ of ${}_{6}^{12}C$ . If the half-life of the decay process is $t_{0}$ , the net energy produced between time, $t = 0$ and $t = 2 t_{0}$ will be nearly,

MEDIUM

Physics>Modern Physics>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

MEDIUM

Physics>Modern Physics>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>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

MEDIUM

Physics>Modern Physics>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:

HARD

Physics>Modern Physics>Nuclei>Radioactivity

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?

Important Questions on Nuclei

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