46: The Nucleus : Neet-xii-physics

Home Learn Fast select Course

Change Unit Change Subject Last Menu

NEET-XII-Physics

46: The Nucleus

with Solutions - page 3

Note: Please signup/signin free to get personalized experience.

10 minutes can boost your percentage by 10%

Note: Please signup/signin free to get personalized experience.

Qstn #14
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
(a) 6 h
(b) 12 h
(c) 24 h
(d) 128 h.
digAnsr: b
Ans : (b) 12 h
A freshly prepared radioactive source emits radiation of intensity that is 64 times the permissible level. This means that it is possible to work safely till 6 half-lives (as 2⁶ = 64) of the radioactive source. Since the half-life of the source is 2h, the minimum time after which it would be possible to work safely with this source is 12 h.
Page No 441:

Qstn #15
The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively
(a) 1/λ and (In 2/λ)
(b) (In 2/λ) and 1/λ
(c) λ(In 2) and 1/λ
(d) λ/(In 2) and 1/λ.
digAnsr: b
Ans : (b) (ln 2/λ) and 1/λ
The half-life of a radioactive sample (`` {t}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}``) is defined as the time elapsed before half the active nuclei decays.
Let the initial number of the active nuclei present in the sample be N₀.
`` \frac{{N}_{o}}{2}={N}_{o}{e}^{-\lambda {t}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}``
`` \Rightarrow {t}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{\,\mathrm{\,ln\,}2}{\lambda }``
Average life of the nuclei, `` {t}_{av}=\frac{S}{{N}_{o}}=\frac{1}{\lambda }``
Here, S is the sum of all the lives of all the N nuclei that were active at t = 0 and `` \lambda `` is the decay constant of the sample.
Page No 441:

Qstn #16
An α-particle is bombarded on ¹⁴N. As a result, a ¹⁷O nucleus is formed and a particle is emitted. This particle is a
(a) neutron
(b) proton
(c) electron
(d) positron.
digAnsr: b
Ans : (b) proton
If an alpha particle is bombarded on a nitrogen (N-14) nucleus, an oxygen (O-17) nucleus and a proton are released.
According to the conservation of mass and charge,
`` {}_{2}{}^{4}He+{}_{7}{}^{14}N\to {}_{6}{}^{17}O+{}_{1}{}^{1}p``
So, the emitted particle is a proton.
Page No 441:

Qstn #17
Ten 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
(a) 10 g
(b) 5 g
(c) 2.5 g
(d) 1.25 g.
digAnsr: a
Ans : (a) 10 g
⁵⁷Co is undergoing beta decay, i.e. electron is being produced. But an electron has very less mass (9.11`` \times ``10^-31kg) as compared to the Co atom. Therefore, after 570 days, even though the atoms undergo large beta decay, the weight of the material in the container will be nearly 10 g.
Page No 441:

Qstn #18
Free ²³⁸U nuclei kept in a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x in time t after the decay. If a decay takes place when the train is moving at a uniform speed v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured by the passenger will be
(a) x + vt
(b) x - vt
(c) x
(d) depends on the direction of the train.
digAnsr: c
Ans : (c) x
When the train is stationary, the separation between the alpha particle and recoiling uranium nucleus is x in time t after the decay. Even if the decay is taking place in a moving train and the separation is measured by the passenger sitting in it, the separation between the alpha particle and nucleus will be x. This is because the observer is also moving with the same speed with which the alpha particle and recoiling nucleus are moving, i.e. they all are in the same frame that is moving at a uniform speed.
Page No 441:

Qstn #19
During a nuclear fission reaction,
(a) a heavy nucleus breaks into two fragments by itself a light nucleus bombarded by thermal neutrons breaks up
(b) a light nucleus bombarded by thermal neutrons breaks up
(c) a heavy nucleus bombarded by thermal neutrons breaks up
(d) two light nuclei combine to give a heavier nucleus and possible other products.
digAnsr: c
Ans : (c) a heavy nucleus bombarded by thermal neutrons breaks up
In a nuclear reactor, a large fissile atomic nucleus like uranium-235 absorbs a thermal neutron and undergoes a nuclear fission reaction. The heavy nucleus splits into two or more lighter nuclei releasing gamma radiation and free neutrons.
Page No 441:

#
Section : iii

Qstn #1
As the mass number A increases, which of the following quantities related to a nucleus do not change?
(a) Mass
(b) Volume
(c) Density
(d) Binding energy
digAnsr: c
Ans : (c) Density
Radius of a nucleus with mass number A is given as
`` R={R}_{o}{A}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}``
Here, R_o = 1.2 fm
∴ Volume of the nucleus = `` \frac{4\pi {R}^{3}}{3}=\frac{4\pi {{R}_{o}}^{3}A}{3}``
This depends on A. With an increase in A, V increases proportionally.
Mass of the nucleus `` \simeq `` Am_N
Here, m_Nis the mass of a nucleon.
Therefore, mass of the nucleus also increases with the increasing mass number.
Binding energy also depends on mass number (number of nucleons) as it is the difference between the total mass of the constituent nucleons and the nucleus. Therefore, it also varies with the changing mass number.
On the other hand,
Density = `` \frac{\,\mathrm{\,Mass\,}}{\,\mathrm{\,Volume\,}}=\frac{A{m}_{N}}{{\displaystyle \raisebox{1ex}{$4\pi {R}^{3}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=\frac{A{m}_{N}}{{\displaystyle \raisebox{1ex}{$4\pi {{R}_{o}}^{3}A$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=\frac{{m}_{N}}{{\displaystyle \raisebox{1ex}{$4\pi {{R}_{o}}^{3}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=\frac{3{m}_{N}}{{\displaystyle 4\pi {{R}_{o}}^{3}}}``
This is independent of A and hence does not change as mass number increases.
Page No 441:

Qstn #2
The heavier nuclei tend to have larger N/Z ratio because
(a) a neutron is heavier than a proton
(b) a neutron is an unstable particle
(c) a neutron does not exert electric repulsion
(d) Coulomb forces have longer range compared to the nuclear forces.
digAnsr: c,d
Ans : (c) a neutron does not exert electric repulsion
(d) Coulomb forces have longer range compared to the nuclear forces
This is because in heavy nuclei, the N/Z ratio becomes larger in order to maintain their stability and reduce instability caused due to the repulsion among the protons.The neutrons exert only attractive short-range nuclear forces on each other as well as on the neighbouring protons, whereas the protons exert attractive short-range nuclear forces on each other as well as the electrostatic repulsive force. Thus, the nuclei with high mass number, in order to be stable, have large neutron to proton ratio (N/Z).
Page No 441:

Qstn #3
A free neutron decays to a proton but a free proton does not decay to a neutron. This is because
(a) neutron is a composite particle made of a proton and an electron whereas proton is a fundamental particle
(b) neutron is an uncharged particle whereas proton is a charged particle
(c) neutron has large rest mass than the proton
(d) weak forces can operate in a neutron but not in a proton.
digAnsr: c
Ans : (c) neutron has large rest mass than the proton.
A nucleus is made up of two fundamental particles- neutrons and protons. If a nucleus has more number of neutrons than what is needed to have stability, then neutrons decay into protons and if there's an excess of protons, then they decay to form neutrons. Since a neutron has larger rest mass than a proton, the Q-value of its decay reaction is positive and a free neutron decays to a proton, while an isolated proton cannot decay to a neutron as the Q-value of its decay reaction is negative. Hence, it is physically not possible.
Page No 441:

Qstn #4
Consider a sample of a pure beta-active material.
(a) All the beta particles emitted have the same energy.
(b) The beta particles originally exist inside the nucleus and are ejected at the time of beta decay.
(c) The antineutrino emitted in a beta decay has zero mass and hence zero momentum.
(d) The active nucleus changes to one of its isobars after the beta decay.
digAnsr: d
Ans : (d) The active nucleus changes to one of its isobars after the beta decay.
In a beta decay, either a neutron is converted to a proton or a proton is converted to a neutron such that the mass number does not change. Also,the number of the nucleons present in the nucleus remains the same. Thus, the active nucleus gets converted to one of its isobars after beta decay.
Page No 441:

Qstn #5
In which of the following decays the element does not change?
(a) α-decay
(b) β⁺-decay
(c) β^--decay
(d) γ-decay
digAnsr: d
Ans : (d) γ-decay
In alpha particle decay, the unstable nucleus emits an alpha particle reducing its proton number Z by 4 and neutron number N by 2 such that the element gets changed.
`` {}_{Z}{}^{A}X\to {}_{Z-2}{}^{A-4}Y+{}_{2}{}^{4}He``
During β^--decay, a neutron is converted to a proton, an electron and an antineutrino, i.e. an active nucleus gets converted to one of its isobars and hence the element gets changed.
`` {}_{Z}{}^{A}X\to {}_{Z+1}{}^{A}Y+e+\stackrel{¯}{\nu }``
During β⁺-decay, a proton in the nucleus is converted to a neutron, a positron and a neutrino in order to maintain the stability of the nucleus, i.e. an active nucleus gets converted to one of its isobars and hence the element gets changed.
`` {}_{Z}{}^{A}X\to {}_{Z-1}{}^{A}Y+{\beta }^{+}+\nu ``
When a nucleus is in higher excited state or has excess of energy, it comes to the ground state in order to become stable and release energy in the form of electromagnetic radiation called gamma ray. Hence, the element in gamma decay doesn't change.
Page No 441:

Qstn #6
In which of the following decays the atomic number decreases?
(a) α-decay
(b) β⁺-decay
(c) β^--decay
(d) γ-decay
digAnsr: a,b
Ans : (a) α-decay

(b) β⁺-decay
In alpha particle decay, the unstable nucleus emits an alpha particle reducing its proton number (atomic number) Z as well as neutron number N by 2.
`` {}_{Z}{}^{A}X\to {}_{Z-2}{}^{A-4}Y+{}_{2}{}^{4}He``
During β^--decay, a neutron is converted to a proton, an electron and an antineutrino. Thus, there is an increase in the atomic number.
`` {}_{Z}{}^{A}X\to {}_{Z+1}{}^{A}Y+{e}^{-}+\stackrel{¯}{\nu }``
During β⁺-decay, a proton in the nucleus is converted to a neutron, a positron and a neutrino in order to maintain the stability of the nucleus. Thus, there is a decrease in the atomic number.
`` {}_{Z}{}^{A}X\to {}_{Z-1}{}^{A}Y+{\beta }^{+}+\nu ``
When a nucleus is in higher excited state or has excess of energy, it comes to the lower state in order to become stable and release energy in the form of electromagnetic radiation called gamma ray. The element in the gamma decay doesn't change.
Therefore, alpha and beta plus decay suffer decrease in atomic number.
Page No 441:

Qstn #7
Magnetic field does not cause deflection in
(a) α-rays
(b) beta-plus rays
(c) beta-minus rays
(d) gamma rays
digAnsr: d
Ans : (d) gamma rays
Magnetic force acts on a charged particle, due to which it deflects from its path. The magnitude of this force is measured as `` \left|\stackrel{\to }{F}\right|=\left|q(\stackrel{\to }{v}\times \stackrel{\to }{B})\right|``.
Here, q is the charge on the particle that is moving with speed v in a uniform magnetic field B.
Since alpha, beta-plus and beta-minus are charged particles, they suffer deflection due to the field applied. On the other hand, gamma rays are photons and due to zero charge, they do not suffer any deflection.
Page No 441:

Qstn #8
Which of the following are electromagnetic waves?
(a) α-rays
(b) Beta-plus rays
(c) Beta-minus rays
(d) Gamma rays
digAnsr: d
Ans : (d) Gamma rays
Alpha rays, beta-plus and beta-minus rays carry charged particles that show particle behaviour. On the other hand, gamma rays carry photons that show particle as well as wave behaviour. Hence, only gamma rays are electromagnetic waves.
Page No 441: