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The Nucleus Physics - The Nucleus

Rajasthan Board (RBSE) - STD 12 Science - Physics (Rajasthan - English Medium). 94 questions in this chapter.

Question types

The Nucleus question types

94 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

94
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6
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5
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Sample Questions

The Nucleus questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Ten grams of $^{57}Co$ 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$:$
  • ✓
    $10g$
  • B
    $5g$
  • C
    $2.5g$
  • D
    $1.25g$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
The mass of a neutral carbon atom in ground state is:
  1. Exact 12u
  2. Less than 12u
  3. More than 12u
  4. Depends on the form of carbon such as graphite or charcoal.
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Q 4M.C.Q (1 Marks)1 Mark
As compared to $^{12}C$ atom $,^{14}C$ atom has:
  • A
    Two extra protons and two extra electrons.
  • B
    Two extra protons but no extra electron.
  • ✓
    Two extra neutrons and no extra electron.
  • D
    Two extra neutrons and two extra electrons.

Answer: C.

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Q 5M.C.Q (1 Marks)1 Mark
The mass number of a nucleus is:
  • A
    Always less than its atomic number.
  • B
    Always more than its atomic number.
  • C
    Equal to its atomic number.
  • ✓
    Sometimes more than and sometimes equal to its atomic number.

Answer: D.

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Q 61 Marks Question1 Mark
Show that the minimum energy needed to separate a proton from a nucleus with $Z$ protons and $N$ neutrons is:
$\Delta\text{E}=(\text{M}_{\text{Z}-1,\text{N}}+\text{M}_{\text{H}}-\text{M}_{\text{Z,N}})\text{c}^2$
where $M_{Z,N} =$ mass of an atom with $Z$ protons and $N$ neutrons in the nucleus and $M_H =$ mass of a hydrogen atom. This energy is known as proton-separation energy.
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Q 71 Marks Question1 Mark
  1. Calculate the energy released if $^{238}U$ emits an $\alpha-$particle.
  2. Calculate the energy to be supplied to $^{238}U$ it two protons and two neutrons are to be emitted one by one. The atomic masses of $^{238}U,\ ^{234}Th$ and $^4He$ are $238.0508u, 234.04363u$ and $4.00260u$ respectively.
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Q 81 Marks Question1 Mark
$^{32}P$ beta-decays to $^{32}S.$ Find the sum of the energy of the antineutrino and the kinetic energy of the $\beta-$particle. Neglect the recoil of the daughter nucleus. Atomic mass of $^{32}P = 31.974u$ and that of $^{32}S = 31.972u.$
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Q 91 Marks Question1 Mark
Calculate the minimum energy needed to separate a neutron from a nucleus with $Z$ protons and $N$ neutrons it terms of the masses $M_{Z.N,} M_{Z,N-1}$ and the mass of the neutron.
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Q 102 Marks Questions2 Marks
The decay constant of $\text{ }^{197}_{80}\text{Hg} ($electron capture to $\text{ }^{197}_{79}\text{Au})$ is $1.8 \times 10^{-4} S^{-1}.$
  1. What is the half-life$?$
  2. What is the average-life$?$
  3. How much time will it take to convert $25\%$ of this isotope of mercury into gold$?$
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Q 112 Marks Questions2 Marks
Complete the following decay schemes.
  1. $\text{ }^{226}_{88}\text{Ra}\rightarrow\alpha+$
  2. $\text{ }^{19}_8\text{O}\rightarrow\text{ }^{19}_9\text{F}+$
  3. $\text{ }^{25}_{13}\text{Al}\rightarrow\text{ }^{25}_{12}\text{Mg}+$
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Q 122 Marks Questions2 Marks
A free neutron beta$-$decays to a proton with a half$-$life of $14$ minutes.
  1. What is the decay constant?
  2. Find the energy liberated in the process.
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Q 132 Marks Questions2 Marks
Lithium $(Z = 3)$ has two stable isotopes $^6Li$ and $^7Li.$ When neutrons are bombarded on lithium sample, electrons and $\alpha-$particles are ejected. Write down the nuclear process taking place.
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Q 142 Marks Questions2 Marks
In the decay $^{64}Cu \rightarrow ^{64}Ni + e^+ + v,$ the maximum kinetic energy carried by the positron is found to be $0.650\ MeV.$
  1. What is the energy of the neutrino which was emitted together with a positron of kinetic energy $0.150\ MeV?$
  2. What is the momentum of this neutrino in $kg-m/s?$
Use the formula applicable to a photon.
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Q 163 Marks Question3 Marks
The count rate from a radioactive sample falls from $4.0 \times 10^6$ per second to $1.0 \times 10^{6 }per$ second in $20$ hours. What will be the count rate $100$ hours after the beginning?
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Q 173 Marks Question3 Marks
$\text{ }^{197}_{80}\text{Hg}$ decay to $\text{ }^{197}_{79}\text{Au}$ through electron capture with a decay constant of 0.257 per day.
  1. What other particle or particles are emitted in the decay?
  2. Assume that the electron is captured from the K shell. Use Moseley's law $\sqrt{\text{v}}=\text{a(Z}-\text{b})$ with $\text{a}=4.95\times10^7\text{s}^{-\frac{1}{2}}$ and b = 1 to find the wavelength of the $\text{K}_{\alpha}$ X-ray emitted following the electron capture.
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Q 183 Marks Question3 Marks
Consider two pairs of neutrons. In each pair, the separation between the neutrons is the same. Can the force between the neutrons have different magnitudes for the two pairs?
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Q 193 Marks Question3 Marks
Calculate the energy released by $1g$ of natural uranium assuming $200MeV$ is released in each fission event and that the fissionable isotope $^{235}U$ has an abundance of $0.7\%$ by weight in natural uranium.
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Q 204 Marks Questions4 Marks
A sample contains a mixture of $^{108}Ag$ and $^{110}Ag$ isotopes each having an activity of $8.0 \times 10^8$ disintegration per second. $^{110}Ag$ is known to have larger half$-$life than $^{108}Ag$. The activity A is measured as a function of time and the following data are obtained.
Time $(s)$ $Activity (A) (10^8 disinte- grations s^{-1})$ Time $(s)$ $Activity (A) (10^8 disinte-grations s^{-1})$
$20$ $11.799$ $200$ $3.0828$
$40$ $9.1680$ $300$ $1.8899$
$60$ $7.4492$ $400$ $1.1671$
$80$ $6.2684$ $500$ $0.7212$
$100$ $5.4115$    
  1. Plot ln $\Big(\frac{\text{A}}{\text{A}_0}\Big)$ versus time.
  2. See that for large values of time, the plot is nearly linear. Deduce the half-life of $^{110}Ag$ from this portion of the plot.
  3. Use the half-life of $^{110}Ag$ to calculate the activity corresponding to $^{108}Ag$ in the first $50s.$
  4. Plot In $\Big(\frac{\text{A}}{\text{A}_0}\Big)$ versus time for $^{108}Ag$ for the first 50s.
  5. Find the half-life of $^{108}Ag.$
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Q 214 Marks Questions4 Marks
The half-life of $^{226}Ra$ is $1602y.$ Calculate the activity of $0.1g$ of $RaCl_2$ in which all the radium is in the form of $^{226}Ra.$ Taken atomic weight of $Ra$ to be $226\ g/mol^{-1}$ and that of $Cl$ to be $35.5\ g/mol^{-1}.$
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Q 235 Marks Questions5 Marks
A vessel of volume $125\ cm^3$ contains tritium $\big(\text{ }^3\text{H,t}_{\frac{1}{2}}=12.3\text{y}\big)$ at $500\ kPa$ and $300K.$ Calculate the activity of the gas.
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Q 255 Marks Questions5 Marks
$^{238}U$ decays to $^{206}Pb$ with a half-life of $4.47 \times 10^9y.$ This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain $2.00\ mg$ of $^{238}U$ and $0.600\ mg$ of $^{206}Pb.$ Assuming that all the lead has come from uranium, find the life of the rock.
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Q 265 Marks Questions5 Marks
In an agricultural experiment, a solution containing 1 mole of a radioactive material $\Big(\text{t}_{\frac{1}{2}}=14.3\text{ days}\Big)$ was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was $1\mu\text{Ci},$ what per cent of activity is transmitted from the root to the fruit in steady state?
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