Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Atoms and Nuclei question

2024 · 31 Jan · Shift 1 · Q87
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Atoms and Nuclei
  5. /2024 · 31 Jan · Shift 1 · Q87

Atoms and Nuclei question

2024 · 31 Jan · Shift 1 · Q87

JEE MainPhysicsAtoms and NucleiNumerical+4 / −1
The mass defect in a particular reaction is 0.4 g0.4 \mathrm{~g}0.4 g. The amount of energy liberated is n×107 kWhn \times 10^7 \mathrm{~kWh}n×107 kWh, where n=n=n=‾\underline{\hspace{2cm}}​. (speed of light =3×108 m/s)\left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)=3×108 m/s)
Numerical answer
View written solutionFree

Correct answer: 1

  1. Use mass-energy equivalence

    The energy liberated is given by E=Δm c2E = \Delta m \, c^2E=Δmc2

  2. Convert mass defect into SI units

    Given mass defect: Δm=0.4 g=0.4×10−3 kg=4×10−4 kg\Delta m = 0.4\,\text{g} = 0.4 \times 10^{-3}\,\text{kg} = 4 \times 10^{-4}\,\text{kg}Δm=0.4g=0.4×10−3kg=4×10−4kg

  3. Substitute the values

    E=(4×10−4)(3×108)2E = (4 \times 10^{-4})(3 \times 10^8)^2E=(4×10−4)(3×108)2

    E=(4×10−4)(9×1016)E = (4 \times 10^{-4})(9 \times 10^{16})E=(4×10−4)(9×1016)

    E=36×1012=3.6×1013 JE = 36 \times 10^{12} = 3.6 \times 10^{13}\,\text{J}E=36×1012=3.6×1013J

  4. Convert joules to kWh

    We know: 1 kWh=3.6×106 J1\,\text{kWh} = 3.6 \times 10^6\,\text{J}1kWh=3.6×106J

    Therefore, Energy in kWh=3.6×10133.6×106=107 kWh\text{Energy in kWh} = \frac{3.6 \times 10^{13}}{3.6 \times 10^6} = 10^7\,\text{kWh}Energy in kWh=3.6×1063.6×1013​=107kWh

  5. Compare with the given form

    Given: E=n×107 kWhE = n \times 10^7\,\text{kWh}E=n×107kWh

    Since E=1×107 kWhE = 1 \times 10^7\,\text{kWh}E=1×107kWh

    therefore, n=1n = 1n=1

  6. Comparison with stored answer

    Stored correct answer = 111

    Our derived answer also is 111.

    Hence, the answer agrees.

PreviousNext

More from Atoms and Nuclei

  • The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :2024 · MCQ
  • A nucleus has mass number A1​ and volume V1​. Another nucleus has mass number A2​ and Volume V2​. If relation between mass number is A2​=4A1​, then V1​V2​​=​.2024 · Numerical
  • The mass of proton, neutron and helium nucleus are respectively 1.0073 u,1.0087 u and 4.0015 u. The binding energy of helium nucleus is :2023 · MCQ
  • A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is πx​×10−17 eVs…2023 · Numerical
  • An electron of a hydrogen like atom, having Z=4, jumps from 4th  energy state to 2nd  energy state. The energy released in this process, will be : (Given Rch =13.6 eV) Where R = Rydberg constant c =…2023 · MCQ
  • Nucleus A having Z=17 and equal number of protons and neutrons has 1.2 MeV binding energy per nucleon. Another nucleus B of Z=12 has total 26 nucleons and 1.8 MeV binding energy per nucleons. The…2023 · Numerical
  • The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is : Includes diagram2023 · MCQ
  • The radius of fifth orbit of the Li++ is ​×10−12 m. Take: radius of hydrogen atom =0.51Ao​2023 · Numerical