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The Nucleus Physics - The Nucleus

Rajasthan Board (RBSE) - STD 11 Science - Physics (Rajasthan - English Medium). 95 questions in this chapter.

Question types

The Nucleus question types

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

95
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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
The decay constant of a radioactive sample is $\lambda.$ The half-life and the average-life of the sample are respectively:

  1. $\frac{1}{\lambda}$ and $\Big(\text{ln}\frac{2}{\lambda}\Big)$

  2. $\Big(\text{ln}\frac{2}{\lambda}\Big)$ and $\frac{1}{\lambda}$

  3. $\lambda(\text{ln}2)$ and $\frac{1}{\lambda}$

  4. $\frac{\lambda}{(\text{ln})2}$ and $\frac{1}{\lambda}$

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Q 3M.C.Q (1 Marks)1 Mark
In which of the following decays the element does not change?

  1. $\alpha-\text{decay}$

  2. $\beta^+-\text{decay}$

  3. $\beta^--\text{decay}$

  4. $\gamma-\text{decay}$

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Q 4M.C.Q (1 Marks)1 Mark
An $\alpha$-particle is bombarded on 14N. As a result, a 17O nucleus is formed and a particle is emitted. This particle is a:
  1. Neutron.
  2. Proton.
  3. Electron.
  4. Positron.
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Q 5M.C.Q (1 Marks)1 Mark
The heavier nuclei tend to have larger $\frac{\text{N}}{\text{Z}}$ ratio because:
  1. A neutron is heavier than a proton.
  2. A neutron is an unstable particle.
  3. A neutron does not exert electric repulsion.
  4. Coulomb forces have longer range compared to the nuclear forces.
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Q 61 Marks Question1 Mark
  1. Calculate the energy released if 238U emits an $\alpha$-particle.
  2. Calculate the energy to be supplied to 238U it two protons and two neutrons are to be emitted one by one. The atomic masses of 238U, 234Th and 4He are 238.0508u, 234.04363u and 4.00260u respectively.
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Q 71 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 MZ,N = mass of an atom with Z protons and N neutrons in the nucleus and MH = mass of a hydrogen atom. This energy is known as proton-separation energy.

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Q 81 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 MZ.N, MZ,N-1 and the mass of the neutron.
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Q 91 Marks Question1 Mark
32P beta-decays to 32S. 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 32P = 31.974u and that of 32S = 31.972u.
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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 × 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
Radioactive 131I has a half-life of 8.0 days. A sample containing 131I has activity $20\mu\text{Ci}$ at t = 0.
  1. What is its activity at t = 4 days?
  2. What is its decay constant at t = 4.0 days?
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Q 122 Marks Questions2 Marks
The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old $\text{ }^{32}\text{P}\big(\text{t}_{\frac{1}{2}}=14.3\text{days}\big)$ source if it was originally purchased for 800 rupees?
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Q 132 Marks Questions2 Marks
57Co decays to 57Fe by $\beta^+-\text{ emission.}$- emission. The resulting 57Fe is in its excited state and comes to the ground state by emitting $\gamma-\text{rays}.$ The half-life of $\beta^+-\text{decay}$ is 270 days and that of the $\gamma-\text{emissions}$ is 10-8 s. A sample of 57Co gives 5.0 × 109 gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 109per second?
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Q 153 Marks Question3 Marks
Carbon (Z = 6) with mass number 11 decays to boron (Z = 5).
  1. Is it a $\beta^+-\text{decay}$ or a $\beta^--\text{decay}?$
  2. The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11?
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Q 163 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 173 Marks Question3 Marks
A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes.
  1. What is the decay constant of the sample?
  2. What is its half-life?
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Q 183 Marks Question3 Marks
The decay constant of 238U is 4.9 × 10-18 S-1.
  1. What is the average-life of 238U?
  2. What is the half-life of 238U?
  3. By what factor does the activity of a 238U sample decrease in 9 × 109 years?
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Q 193 Marks Question3 Marks
Radioactive isotopes are produced in a nuclear physics experiment at a constant rate $\frac{\text{dN}}{\text{dt}}=\text{R}.$ An inductor of inductance 100mH, a resistor of resistance $100\Omega$ and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that $\frac{\text{i}}{\text{N}}$ remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.
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Q 204 Marks Question4 Marks
A sample contains a mixture of 108Ag and 110Ag isotopes each having an activity of 8.0 × 108 disintegration per second. 110Ag is known to have larger half-life than 108Ag. The activity A is measured as a function of time and the following data are obtained.
Time (s) Activity (A) (108 disinte- grations s-1)
 Time (s) Activity (A) (108 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 110Ag from this portion of the plot.
  3. Use the half-life of 110Ag to calculate the activity corresponding to 108Ag in the first 50s.
  4. Plot In $\Big(\frac{\text{A}}{\text{A}_0}\Big)$ versus time for 108Ag for the first 50s.
  5. Find the half-life of 108Ag.
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Q 214 Marks Question4 Marks
The half-life of 226Ra is 1602y. Calculate the activity of 0.1g of RaCl2 in which all the radium is in the form of 226Ra. Taken atomic weight of Ra to be 226g/mol-1 and that of Cl to be 35.5g/mol-1.
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Q 225 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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Q 235 Marks Questions5 Marks
$\text{ }^{212}_{33}\text{Bi}$ can disintegrate either by emitting an $\alpha$-particle of by emitting a $\beta^-$-particle.
  1. Write the two equations showing the products of the decays.
  2. The probabilities of disintegration $\alpha$ and $\beta$ -decays are in the ratio $\frac{7}{13}.$ The overall half-life of 212Bi is one hour. If 1g of pure 212Bi is taken at 12.00 noon, what will be the composition of this sample at 1P.m. the same day?
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Q 245 Marks Questions5 Marks
Natural water contains a small amount of tritium $\big(\text{ }^3_1\text{H}\big).$ This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the $\text{}^3_1\text{H}$ radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.
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Q 255 Marks Questions5 Marks
A sample contains a mixture of 108Ag and 110Ag isotopes each having an activity of 8.0 × 108 disintegration per second. 110Ag is known to have larger half-life than 108Ag. The activity A is measured as a function of time and the following data are obtained.
Time (s) Activity (A) (108 disinte- grations s-1)
 Time (s) Activity (A) (108 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 110Ag from this portion of the plot.
  3. Use the half-life of 110Ag to calculate the activity corresponding to 108Ag in the first 50s.
  4. Plot In $\Big(\frac{\text{A}}{\text{A}_0}\Big)$ versus time for 108Ag for the first 50s.
  5. Find the half-life of 108Ag.
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