Radioactivity

Interactive Feed

The intensity of gamma radiation from a given source is $I$ . On passing through $36 mm$ of lead, it is reduced to $I /8$ . The thickness of lead, which will reduce the intensity to $I /2$ will be

6 mm

(B)

9 mm

(C)

18 mm

(D)

12 mm

JEE Advanced 2012

LEVELJEE Advanced

Comprehension Passage

The

β

-decay process, discovered around 1900, is basically the decay of a neutron (

n

). In the laboratory, a proton (

p

) and an electron (

e^{-}

) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a continuous spectrum. Considering a three-body decay process, i.e.,

n \to p + e^{-} + \overset{ν}{ˉ}_{e}

, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino (

\overset{ν}{ˉ}_{e}

) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is

0.8 \times 1 0^{6}

eV. The kinetic energy carried by the proton is only the recoil energy.

Question 1:

If the anti-neutrino had a mass of $3 eV / c^{2}$ (where $c$ is the speed of light) instead of zero mass, what should be the range of the kinetic energy $K$ , of the electron?

(A)

0 \leq K \leq 0.8 \times 1 0^{6} eV

(B)

3.0 eV \leq K \leq 0.8 \times 1 0^{6} eV

(C)

3.0 eV \leq K < 0.8 \times 1 0^{6} eV

(D)

0 \leq K < 0.8 \times 1 0^{6} eV

Question 2:

What is the maximum energy of the anti-neutrino?

0.8 \times 1 0^{6} eV

(C)

Nearly

0.8 \times 1 0^{6} eV

(D)

Much larger than

0.8 \times 1 0^{6} eV

LEVELBoard

Which of the following is a correct statement ?

(A)

Beta rays are same as cathode rays

(B)

Gamma rays are high energy neutrons

(C)

Alpha particles are singly ionized helium atoms

(D)

Protons and neutrons have exactly the same mass

LEVELJEE Main

After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is

Which of the following processes represent a $γ$ -decay ?

(A)

_{Z}^{A} X + γ \to_{Z - 1}^{A} X + a + b

(B)

_{Z}^{A} X +_{0}^{1} n \to_{Z - 2}^{A - 3} X + c

(C)

_{Z}^{A} X \to_{Z}^{A} X + f

(D)

_{Z}^{A} X + e_{- 1} \to_{Z - 1}^{A} X + g

JEE Advanced 2003

LEVELJEE Advanced

A radioactive element decays by $β$ -emission. A detector records $n$ beta particles in $2 s$ and in next $2 s$ it records $0.75 n$ beta particles. Find mean life of the radioactive element. Given $ln ∣2∣ = 0.6931, ln ∣3∣ = 1.0986$ .

JEE Advanced 1998

LEVELJEE Advanced

Nuclei of a radioactive element $A$ are being produced at a constant rate $α$ . The element has a decay constant $λ$ . At time $t = 0$ , there are $N_{0}$ nuclei of the element. (a) Calculate the number $N$ of nuclei of $A$ at time $t$ . (b) If $α = 2 N_{0} λ$ , calculate the number of nuclei of $A$ after one half-life of $A$ and also the limiting value of $N$ as $t \to \infty$ .

LEVELJEE Main

$^{22} Ne$ nucleus, after absorbing energy, decays into two $α$ -particles and an unknown nucleus. The unknown nucleus is

A nucleus $X$ , initially at rest, undergoes alpha-decay according to the equation. $_{92}^{A} X \to_{Z}^{228} Y + α$ (a) Find the values of $A$ and $Z$ in the above process. (b) The alpha particle produced in the above process is found to move in a circular track of radius $0.11 m$ in a uniform magnetic field of $3 T$ . Find the energy (in MeV) released during the process and the binding energy of the parent nucleus $X$ . Given that $m (Y) = 228.03 u$ ; $m (_{0}^{1} n) = 1.009 u$ ; $m (_{2}^{4} He) = 4.003 u$ ; $m (_{1}^{1} H) = 1.008 u$ .

LEVELJEE Main

The half-life of the radioactive radon is 3.8 days. The time, at the end of which 1/20th of the radon sample will remain undecayed, is (given $lo g_{10} e = 0.4343$ )

A nucleus with mass number 220 initially at rest emits an $α$ -particle. If the $Q$ value of the reaction is 5.5 MeV, calculate the kinetic energy of the $α$ -particle

The element curium $_{96}^{248} Cm$ has a mean life of $1 0^{13} s$ . 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 : $_{96}^{248} Cm = 248.072220 u$ , $_{94}^{244} Pu = 244.064100 u$ and $_{2}^{4} He = 4.002603 u$ . Calculate the power output from a sample of $1 0^{20} Cm$ atoms. ( $1 u = 931 MeV / c^{2}$ )

JEE Advanced 2017

LEVELJEE Advanced

$^{131} I$ is an isotope of Iodine that decays into an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with $^{131} I$ is injected into the blood of a person. The activity of the amount of $^{131} I$ injected was $2.4 \times 1 0^{5}$ Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 h, 2.5 ml of blood is drawn from the person's body, and gives an activity of 115 Bq. The total volume of blood in the person's body, in litres is approximately (you may use $e^{x} \approx 1 + x$ for $∣ x ∣ ≪ 1$ and $ln 2 \approx 0.7$ ).

LEVELJEE Main

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 $1/ e$ after a time

(A)

\frac{1}{10 λ}

(B)

\frac{1}{11 λ}

(C)

\frac{11}{10 λ}

(D)

\frac{1}{9 λ}

LEVELBoard

Beta rays emitted by a radioactive material are

(A)

electromagnetic radiations

(B)

the electrons orbiting around the nucleus

(C)

charged particles emitted by the nucleus

A rock is $1.5 \times 1 0^{9}$ yr old. The rock contains $^{238} U$ which disintegrates to form $^{206} Pb$ . Assume that there was no $^{206} Pb$ in the rock initially and it is the only stable product formed by the decay. Calculate the ratio of number of nuclei of $^{238} U$ to that of $^{206} Pb$ in the rock. Half-life of $^{238} U$ is $4.5 \times 1 0^{9}$ yr. ( $2^{1/3} = 1.259$ )

LEVELJEE Main

The radioactive decay rate of a radioactive element is found to be $1 0^{3}$ disintegration/second at a certain time. If the half-life of the element is one second, the decay rate after one second is ....... and after three seconds is........ .

JEE Advanced 2018

LEVELJEE Main

In a radioactive decay chain, $_{90}^{232} Th$ nucleus decays to $_{82}^{212} Pb$ nucleus. Let $N_{α}$ and $N_{β}$ be the number of $α$ and $β$ - particles respectively, emitted in this decay process. Which of the following statements is (are) true?

* Multiple Correct Options

(A)

N_{α} = 5

(B)

N_{α} = 6

(C)

N_{β} = 2

(D)

N_{β} = 4

LEVELJEE Main

A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

The decay constant of a radioactive sample is $λ$ . The half-life and mean-life of the sample are respectively given by

(A)

\frac{1}{λ}

and

\frac{l n 2}{λ}

(B)

\frac{l n 2}{λ}

and

\frac{1}{λ}

(C)

λ (ln 2)

and

\frac{1}{λ}

(D)

\frac{λ}{l n 2}

and

\frac{1}{λ}

JEE Advanced 2001

LEVELJEE Advanced

A nucleus at rest undergoes a decay emitting an $α$ -particle of de-Broglie wavelength, $λ = 5.76 \times 1 0^{- 15} m$ . If the mass of the daughter nucleus is $223.610 amu$ and that of the $α$ -particle is $4.002 amu$ . Determine the total kinetic energy in the final state. Hence obtain the mass of the parent nucleus in amu. ( $1 amu = 931.470 MeV / c^{2}$ )

LEVELJEE Main

Masses of two isobars $_{29}^{64} Cu$ and $_{30}^{64} Zn$ are $63.9298 u$ and $63.9292 u$ respectively. It can be concluded from these data that

(A)

both the isobars are stable

(B)

Zn^{64}

is radioactive, decaying to

Cu^{64}

through

β

-decay

(C)

Cu^{64}

is radioactive, decaying to

Zn^{64}

through

γ

-decay

(D)

Cu^{64}

is radioactive, decaying to

Zn^{64}

through

β

-decay

LEVELJEE Main

Consider $α$ -particles, $β$ -particles and $γ$ -rays each having an energy of $0.5 MeV$ . In increasing order of penetrating powers, the radiations are

(A)

α, β, γ

(B)

α, γ, β

(C)

β, γ, α

(D)

γ, β, α

LEVELJEE Main

The half-life of $^{215} At$ is $100 μ s$ . The time taken for the activity of a sample of $^{215} At$ to decay to $\frac{1}{16} th$ of its initial value is

(A)

400 μ s

(B)

63 μ s

(C)

40 μ s

(D)

300 μ s

LEVELJEE Main

The electron emitted in beta radiation originates from

(A)

inner orbits of atom

(B)

free electrons existing in nuclei

(C)

decay of a neutron in a nucleus

(D)

photon escaping from the nucleus

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the anti-neutrino had a mass of 3 eV/c2 (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy K, of the electron?

What is the maximum energy of the anti-neutrino?

Which of the following is a correct statement ?

After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Which of the following processes represent a γ-decay ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 22Ne nucleus, after absorbing energy, decays into two α-particles and an unknown nucleus. The unknown nucleus is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The half-life of the radioactive radon is 3.8 days. The time, at the end of which 1/20th of the radon sample will remain undecayed, is (given log10​e=0.4343)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A nucleus with mass number 220 initially at rest emits an α-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α-particle

Beta rays emitted by a radioactive material are

A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The decay constant of a radioactive sample is λ. The half-life and mean-life of the sample are respectively given by

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Masses of two isobars 2964​Cu and 3064​Zn are 63.9298 u and 63.9292 u respectively. It can be concluded from these data that

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider α-particles, β-particles and γ-rays each having an energy of 0.5 MeV. In increasing order of penetrating powers, the radiations are

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The half-life of 215At is 100μs. The time taken for the activity of a sample of 215At to decay to 161​th of its initial value is

The electron emitted in beta radiation originates from

If the anti-neutrino had a mass of $3 eV / c^{2}$ (where $c$ is the speed of light) instead of zero mass, what should be the range of the kinetic energy $K$ , of the electron?

Which of the following processes represent a $γ$ -decay ?

$^{22} Ne$ nucleus, after absorbing energy, decays into two $α$ -particles and an unknown nucleus. The unknown nucleus is

The half-life of the radioactive radon is 3.8 days. The time, at the end of which 1/20th of the radon sample will remain undecayed, is (given $lo g_{10} e = 0.4343$ )

A nucleus with mass number 220 initially at rest emits an $α$ -particle. If the $Q$ value of the reaction is 5.5 MeV, calculate the kinetic energy of the $α$ -particle

The decay constant of a radioactive sample is $λ$ . The half-life and mean-life of the sample are respectively given by

Masses of two isobars $_{29}^{64} Cu$ and $_{30}^{64} Zn$ are $63.9298 u$ and $63.9292 u$ respectively. It can be concluded from these data that

Consider $α$ -particles, $β$ -particles and $γ$ -rays each having an energy of $0.5 MeV$ . In increasing order of penetrating powers, the radiations are

The half-life of $^{215} At$ is $100 μ s$ . The time taken for the activity of a sample of $^{215} At$ to decay to $\frac{1}{16} th$ of its initial value is