# Beta Decay

## Trending Questions

**Q.**

State the law of radioactive decay. Hence derive the expression $N={N}_{0}{e}^{-\lambda t}$ where symbols have their usual meaning

**Q.**The oscillating frequency of a cyclotron is 10 MHz. If the radius of its dees is 0.5 m, then the kinetic energy of a proton accelerated by the cyclotron will be:

- 5.2 MeV
- 7.2 MeV
- 4.1 MeV
- 2.3 MeV

**Q.**

The anion ${\mathrm{X}}^{3-}$has 18 electrons and its mass number is 31.How many neutrons are present in the nucleus ?

18

8

31

16

**Q.**

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei and from the following data:

= 39.962591 u

) = 40.962278 u

= 25.986895 u

) = 26.981541 u

**Q.**

A nucleus X emits a beta particle to produce a nucleus Y. If their atomic masses are Mx and My respectively. The maximum energy of the beta particle emitted is (Hint: β− decay)

(where me is the mass of an electron and c is the velocity of light)

- (Mx−My−me)c2
- (Mx−My+me)c2
- (Mx−My)c2
- (Mx−My−2me)c2

**Q.**

The
radionuclide ^{11}C
decays according to

The maximum energy of the emitted positron is 0.960 MeV.

Given the mass values:

calculate
*Q
*and
compare it with the maximum energy of the positron emitted

**Q.**When a nucleus with atomic number Z and mass number A undergoes a radioactive decay process,

(1) Both Z and A will decrease, if the process is α decay.

(2) Z will decrease, but A will not change, if the process is β+ decay.

(3) Z will increase, but A will not change, if the process is β− decay.

(4) Z and A will remain unchanged, if the process is γ decay.

- 1 & 2 are true
- 3 & 4 are true
- 1, 2 & 3 are true
- All are true

**Q.**In the given nuclear reaction, A, B, C, D, E represents

92U238α⟶ BThAβ⟶ DPaCE⟶ 92U234

- A=234, B=90, C=234, D=91, E=β
- A=234, B=90, C=238, D=94, E=α
- A=234, B=90, C=234, D=93, E=α
- A=238, B=93, C=234, D=91, E=β

**Q.**In the given reaction

zXA→z+1YA→z−1KA−4→z−1KA−4

Radioactive radiations are emitted in the sequence of

- α, β, γ
- β, α, γ
- γ, α, β
- β, γ, α

**Q.**If a nucleus AZX emits an α− particle and a β− particle, then the daughter nucleus will have the total number of neutrons as A−Z−n=y. The value of n is

**Q.**Why is it difficult to experimentally detect neutrinos in nuclear β-decay ?

**Q.**

The decomposition of the Formic acid on gold surface follows first order kinetics if the rate constant at $300\mathrm{K}$ is $1.0\times {10}^{-3}{\mathrm{s}}^{-1}$ and the activation energy${\mathrm{E}}_{\mathrm{a}}=11.488\mathrm{kJ}{\mathrm{mol}}^{-1}$, then the rate constant at $200\mathrm{K}$ is:__________×10^{–5 }s^{–1 }

**Q.**If ′f′ denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t=0 (N0) then for a collection of radioactive nuclei, the rate of change of ′f′ with respect to time is given as :

[λ is the radioactive decay constant]

- −λe−λt
- −λ(1−e−λt)
- λe−λt
- λ(1−e−λt)

**Q.**

The
*Q
*value
of a nuclear reaction *A
*+
*b
*→ *C
*+
*d
*is
defined by

*Q
*=
[ *m*_{A}+
*m*_{b}−
*m*_{C}−
*m*_{d}]*c*^{2
}where
the masses refer to the respective nuclei. Determine from the given
data the *Q*-value
of the following reactions and state whether the reactions are
exothermic or endothermic.

(i)

(ii)

Atomic masses are given to be

**Q.**A radioactive substance is being produced at a constant rate of 200 nuclei. The decay constant of the substance is 1 s−1. Assuming that initially there are no nuclei present, the time (in second) after which the number of nuclei will become 100 is

- 1 s
- ln(2) s
- 1ln(2) s
- 2 s

**Q.**A certain stable nuclide after absorbing a neutron, emits β− particle and the new nuclide formed splits spontaneously into two α− particles. The nuclide is-

- 3Li6
- 4Be6
- 3Li7
- 2He4

**Q.**The correct statement is

- The nucleus 21084Po can emit a proton
- Deuteron and alpha particle can undergo complete fusion
- The nucleus 63Li can emit an alpha particle
- The nuclei 7030Zn and 8234Se can undergo complete fusion

**Q.**

In β-decay, the Q-value of the process is E. Then

KE of a beta-particle cannot exceed E.

KE of anti-neutrino emitted lies between zero and E

NZ ratio of the nucleus is altered.

Mass number (A) of the nucleus is altered.

**Q.**

A radioactive nucleus undergoes a series of decays according to the sequence.

$\mathrm{X}\stackrel{\mathrm{\beta}}{\to}{\mathrm{X}}_{1}\stackrel{\mathrm{\alpha}}{\to}{\mathrm{X}}_{2}\stackrel{\mathrm{\alpha}}{\to}{\mathrm{X}}_{3}\to $

If the mass number and atomic number of ${\mathrm{X}}_{3}$ are $132$ and $69$ respectively, what is the mass number and atomic number of$X$?

**Q.**Calculate the Q value in the following decay using the atomic masses given in the table.

25Al→25Mg+e++ν

Mass of 25Al | Mass of 25Mg |

24.990432 u | 24.985839 u |

[Take melectron=0.511 MeVc2; c2=931 MeVu]

- 14.816 MeV
- 12.408 MeV
- 11.204 MeV
- 3.254 MeV

**Q.**A copper wire of cross-sectional area 0.01 cm2 is under a tension of 20 N. Find the decrease in the cross-sectional area. Young's modulus and Poisson's ratio of copper are 1.1×1011 N/m2 and 0.32 respectively.

- 3.16×10−6 cm2
- 1.16×10−6 cm2
- 4.16×10−6 cm2
- 2.16×10−6 cm2

**Q.**

For the (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K−shell, is captured by the nucleus and a neutrino is emitted).

Show that if emission is energetically allowed, electron capture is necessarily allowed but not vice−versa.

**Q.**

What is the role of neutrons in the nucleus, as protons are held by pi-meson, what does neutrons do?

**Q.**

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei and from the following data:

= 39.962591 u

) = 40.962278 u

= 25.986895 u

) = 26.981541 u

**Q.**The figure below shows a steel rod of 25 mm2 cross sectional area. It is loaded at four points. K, L, M and N. Assume Esteel = 200 GPa. The total change in length of the rod due to loading is

- 1 μm

- −10 μm
- 1 μm
- −20 μm

**Q.**Which of the following rays is not deflected by a magnetic field?

- α−rays
- β−rays
- γ−rays
- None of these

**Q.**Consider the beta decay

198Au→ 198Hg∗+β−+¯¯¯ν

Where 198Hg∗ represents a mercury nucleus in an excited state at energy 1.088 MeV above the ground state. What can be the maximum kinetic energy of the electron emitted? The atomic mass of 198Au is 197.968233 u and that of 198Hg is 197.966760 u. c2=931 MeVu

- 0.28 MeV
- 5.86 MeV
- 9.25 MeV
- 15.89 MeV

**Q.**

Write nuclear reaction equations for

(i)
*α*-decay
of
(ii)
*α*-decay
of

(iii)
*β*^{−}-decay
of
(iv)
*β*^{−}-decay
of

(v)
*β*^{+}-decay
of
(vi)
*β*^{+}-decay
of

(vii) Electron capture of

**Q.**10 grams of 57Co kept in an open container beta-decays with a half-life of 270 days. The weight of the material inside the container after 540 days will be very nearly.

- 10g
- 5g
- 25g
- 125g

**Q.**

An alpha particle $\left({}_{2}{}^{4}\mathrm{He}\right)$ has a mass of $4.00300amu$. A proton has mass of $1.00783amu$ and a neutron has mass of $1.00867amu$ respectively. The binding energy of alpha particles estimated from these data is the closest to:

$20.4MeV$

$32.0MeV$

$24.3MeV$

$27.9MeV$