When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as { _{ 92 }^{ }{ U } }^{ 235 }+{ _{ 0 }^{ }{ n } }^{ 1 }\longrightarrow { _{ 56 }^{ }{ Ba } }^{ 141 }+{ _{ 36 }^{ }{ Kr } }^{ 92 }+3x+Q(energy) Where three particles named x are produced and energy Q is released. What is the name of the particle x ?

given reaction, _{92} U^{235} + \, _0n^1 \rightarrow \, _{56} Ba^{141} + \, _{36}Kr^{92} + 3x + Q (energy) \sum Atomic number on L.H.S. = 92 + 0 = 92 \sum Atomic number on R.H.S. = 56 + 36 = 92 \therefore number of protons on L.H.S. are equal to the number of protons on R.H.S. hence x not contains protons in it. \sum Atomic mass number on L.H.S. = 235 + 1 = 236 \sum Atomic mass number on R.H.S = 141 + 92 + 3x = 233 + 3x L.H.S = R.H.S 233+ 3x = 236 x=1 Mass number =1 , no. of proton =0 therefor particle will be Neutron.

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

_{90}^{232} Th has converted into _{82}^{212}Pb Change in mass number (A) = 20 \therefore no of \alpha particle = \dfrac{20}{4} = 5 Due to 5 \alpha particle, z will change by 10 unit. Since given change is 8 , therefore no. of the beta particle is 10-8=2

Suppose a ^{226}_{88} Ra nucleus at rest and in ground state undergoes \alpha -decay to a ^{222}_{86} Rn nucleus in its excited state. The kinetic energy of the emitted \alpha particle is found to be 4.44 MeV . ^{222}_{86} Rn nucleus then goes to its ground state by \gamma -decay. The energy of the emitted \gamma photon is ____ keV..[Given : atomic mass of ^{226}_{88}Ra = 226.005 u , atomic mass of ^{222}_{88}Rn = 222.000 u , atomic mass of \alpha particle = 4.000 u, \, 1 u = 931 MeV/c^2, c is speed of light]

Mass defect \Delta m = 226.005 - 222.000 - 4.000 = 0.005 \, amu \therefore Q value = 0.005 \times 931.5 = 4.655 MeV Also \dfrac{K.E_{\alpha}}{K.E_{Rn}} = \dfrac{m_{Rn}}{m_{\alpha}} \Rightarrow K.E_{Rn} = \dfrac{m_{\alpha}}{m_{Rn}} . K.E_{\alpha} = \dfrac{4}{222} \times 4.44 = 0.08 MeV \therefore Energy of \gamma -Photon = 4.655 - (4.44 + 0.08) = 0.135 MeV = 135 KeV

Nuclei - Types Of Questions

Q: Two isotopes P and Q of atomic weight 10 and 20, respectively are mixed in equal amount by weight. After 20 days their weight ratio is found to be 1 : 4. Isotope P has a half-life of 10 days. The half-life of isotope Q is

Let Wg of each be taken initid modes of P \begin{array}{l} =\frac { W }{ { 10 } } \\ \emptyset =\frac { W }{ { 20 } } \\ FindP=\frac { { { W_{ 1 } } } }{ { 5\times 10 } } \\ \emptyset =\frac { { 4{ W_{ 1 } } } }{ { 20\times 5 } } \\ \therefore for\, \, { P_{ 1 } }\frac { { W\times 5\times 10 } }{ { 10{ W_{ 1 } } } } ={ \ell ^{ \times P\times 20 } }\to (i) \\ for\, \, \emptyset { { 1pt }_{ 1 } }\frac { { W\times 20\times 5 } }{ { 20\times { W_{ 1 } }\times 4 } } ={ \ell ^{ \lambda \emptyset \times 20 } }\to (ii) \\ from\, \, \left( 1 \right) \, \& \, \, \left( 2 \right) \\ 4{ \ell ^{ \left( { \lambda P-\lambda \emptyset } \right) \times 20 } } \\ 20\left( { \lambda P-\lambda \emptyset } \right) =\log { e^{ 4 } } \\ 20\left( { \frac { { 0.693 } }{ { { t_{ \frac { 1 }{ 2 } } } } } -\frac { { 0.693 } }{ { 10 } } } \right) =\log { e^{ 4 } } \\ { t_{ \frac { 1 }{ 2 } } }=5 \end{array}

Q: In an experiment the initial number of radioactive nuclei is 3000 . It is found that 1000\pm 40 nuclei decayed in the 1.0\ s . For |x| < < 1, \ln(1+x) = x up to first power in x . The error \Delta \lambda , in the determination of the decay constant \lambda , is s^{-1} , is

N = N_{o} e ^{-\lambda t} ln N = lnN_{o} - \lambda t \dfrac{dN}{N} = - \lambda t Converting to error \dfrac{\Delta N}{N} = \Delta \lambda t \Delta \lambda = \dfrac{40}{2000 \times L} =0.02

Q: Mark out the correct statement(s)

For (a) as the mass of alpha particle is less than that of daughter nucleus the speed of alpha particle will be more to conserve momentum and thus more kinetic energy.For (b) In beta decay, the change in binding energy appears as the mass-energy and kinetic energy of the beta particle, the energy of the neutrino, and the kinetic energy of the recoiling daughter nucleus.For (c) the energy released in beta minus decay is shared between electron and antineutrino as the kinetic energyFor (d) the energy released is in the form of gamma radiation

Q: The isotope _{ 5 }^{ 12 }{ B } having a mass 12.014 u undergoes \beta -decay to _{ 6}^{ 12 }{ C } , _{ 6 }^{ 12 }{ C } has an excited state of the nucleus ( _{ 5 }^{ 12 }{ C^* } ) at 4.041 MeV above its ground state. If _{ 5 }^{ 12 }{ B } decays to _{ 6 }^{ 12 }{ C^* } , the maximum kinetic energy of the \beta -particle in units of MeV is(1 u = 931.5 MeV/ { c }^{ 2 } , where c is the speed of light in vacuum).

_{ 5 }^{ 12 }B\rightarrow _{ 6 }^{ 12 }{ C }+{ \beta }^{ - }+{ \gamma }^{ - } Q=(m_{ 5 }^{ 12 }{ B }-m_{ 6 }^{ 12 }{ C }){ c }^{ 2 }\\ \quad =(m_{ 5 }^{ 12 }{ B }-(m_{ 6 }^{ 12 }{ C }+\Delta m)){ c }^{ 2 }\\ \quad =(m_{ 5 }^{ 12 }{ B }-m_{ 6 }^{ 12 }{ C }){ c }^{ 2 }-\Delta m{ c }^{ 2 }\\ \quad =0.014\times 931.5-4.041\\ \quad =9\ MeV

Q: In Column I consider each process just before and just after it occurs. Initial system is isolated from all other bodies. Consider all product particles (even those having rest mass zero) in the system. Match the system in Column I with the result they produce in Column II

A _{ 92 }^{ 238 }{ U }\rightarrow _{ 90 }^{ 234 }{ Th }+_{ 2 }^{ 4 }{ He } #Proton is conserved.#Momentum is always conserved in absence of external force.#Since reaction is spontaneous so mass is converted into energy.#Charge is always conservedSo, (A)\rightarrow(2),(3),(4) B _{ 92 }^{ 238 }{ U }\rightarrow _{ 90 }^{ 234 }{ Th }+_{ 2 }^{ 4 }{ He } #Proton is conserved.#Momentum is always conserved in absence of external force.#Since reaction is spontaneous so mass is converted into energy.#Charge is always conservedSo, (B)\rightarrow(2),(3),(4) C _{ 92 }^{ 238 }{ U }\rightarrow _{ 90 }^{ 234 }{ Th }+_{ 2 }^{ 4 }{ He } #Proton is conserved.#Momentum is always conserved in absence of external force.#Since reaction is spontaneous so mass is converted into energy.#Charge is always conservedSo, (C)\rightarrow(2),(3),(4) D In \beta^- decay proton increases by +1Here, other atom is not given so (2) will not be the answer.So, (D)\rightarrow(1),(3),(4)

Q: Match the following Columns.

Both fission and fusion are nucleus reactions that produce energy, but the application are not same. Fission is the splitting of heavy unstable nucleus into two lighter nuclie and fusion is the process where two light nuclie combine together releasing vast amount of energy. \beta decay produce energy. \beta decay is a consequence of weak force characterized by lengthy decay time.Exothermic nuclear reaction produce energy as the name suggest Exo (heat)Two light nuclie fuse together (fusion reaction) Here mass of resulting nucleus is lower than mass of two reacting nuclie so energy is released.It may be fusion or fission reaction.

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Types Of Questions

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Nuclei

- Wondering what kind of questions that can be asked in next exam? Here you go!

JEE Advanced

Single choice correct

When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as

_{92} U^{235} +_{0} n^{1} ⟶_{56} B a^{141} +_{36} K r^{92} + 3 x + Q (e n e r g y)

Where three particles named

x

are produced and energy

Q

is released. What is the name of the particle

x

electron

α

- particle

neutron

neutrino

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Two isotopes P and Q of atomic weight 10 and 20, respectively are mixed in equal amount by weight. After 20 days their weight ratio is found to be 1 : 4. Isotope P has a half-life of 10 days. The half-life of isotope Q is

zero

5 days

20 days

infinite

View solution

In an experiment the initial number of radioactive nuclei is

3000

. It is found that

1000 \pm 40

nuclei decayed in the

1.0 s

. For

∣ x ∣ < < 1, ln (1 + x) = x

up to first power in

x

. The error

Δ λ

, in the determination of the decay constant

λ

, is

s^{- 1}

, is

0.04

0.03

0.02

0.01

View solution

Multiple choice correct

In a radioactive decay chain,

_{90}^{232} T h

nucleus decays to

_{82}^{212} P b

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?

This question has multiple correct options

N_{α} = 5

N_{α} = 6

N_{β} = 2

N_{β} = 4

View solution

Mark out the correct statement(s)

This question has multiple correct options

In alpha decay, the energy released is shared between alpha particle and daughter nucleus in the form of kinetic energy and share of alpha particle is more than that of the daughter

In beta decay, the energy released in the form of kinetic energy of beta particles

In beta minus decay, the energy released is shared between electron and antineutrino

In gamma decay, the energy released is in the form of energy carried by photons termed as gamma rays

View solution

Blank Type

The isotope

_{5}^{12} B

having a mass 12.014 u undergoes

β

-decay to

_{6}^{12} C

_{6}^{12} C

has an excited state of the nucleus (

_{5}^{12} C^{*}

) at 4.041 MeV above its ground state. If

_{5}^{12} B

decays to

_{6}^{12} C^{*}

, the maximum kinetic energy of the

β

-particle in units of MeV is
(1 u = 931.5 MeV/

c^{2}

, where c is the speed of light in vacuum).

View solution

Suppose a

_{88}^{226} R a

nucleus at rest and in ground state undergoes

α

-decay to a

_{86}^{222} R n

nucleus in its excited state. The kinetic energy of the emitted

α

particle is found to be

4.44 M e V

_{86}^{222} R n

nucleus then goes to its ground state by

γ

-decay. The energy of the emitted

γ

photon is ____ keV..
[Given : atomic mass of

_{88}^{226} R a = 226.005 u

, atomic mass of

_{88}^{222} R n = 222.000 u

, atomic mass of

α

particle =

4.000 u, 1 u = 931 M e V / c^{2}, c

is speed of light]

View solution

Matrix Match type

In Column I consider each process just before and just after it occurs. Initial system is isolated from all other bodies. Consider all product particles (even those having rest mass zero) in the system. Match the system in Column I with the result they produce in Column II

List 1Spontaneous radioactive decay of a uranium nucleus initially at rest as given by reaction

_{92}^{238} U \to_{90} 234 T h +_{2}^{4} H e + . . . .

Fusion reaction of two hydrogen nuclei as given by reaction

_{1}^{1} H +_{1}^{1} H \to_{1}^{2} H + . . . .

Fission of

U^{235}

nucleus initiated by a thermal neutron as given by reaction

_{0}^{1} n +_{92}^{235} U \to_{56}^{144} B a +_{36}^{89} K + 3_{0}^{1} n + . . .

β - d e c a y

(negative beta decay)

List 2Number of protons is increasedMomentum is conservedMass is converted to energy or vice versaCharge is conserved

View solution

Match the following Columns.

List 1Nuclear fusionNuclear fission

β - d e c a y

Exothermic nuclear reaction

List 2Releases energyGenerally possible for nuclei withlow atomic numberGenerally possible for nuclei with higher atomic numberIs caused due to nuclear fission

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