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Atoms and Nuclei question

2024 · 9 Apr · Shift 1 · Q76
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Atoms and Nuclei question

2024 · 9 Apr · Shift 1 · Q76

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1
The energy equivalent of 1 g1 \mathrm{~g}1 g of substance is :
  1. A
    5.6×1026 MeV5.6 \times 10^{26} \mathrm{~MeV}5.6×1026 MeV
  2. B
    5.6×1012 MeV5.6 \times 10^{12} \mathrm{~MeV}5.6×1012 MeV
  3. C
    5.6 eV5.6 \mathrm{~eV}5.6 eV
  4. D
    11.2×1024 MeV11.2 \times 10^{24} \mathrm{~MeV}11.2×1024 MeV
View written solutionFree

Correct answer: A

  1. Use Einstein’s mass-energy relation:

E=mc2E = mc^2E=mc2

For 1 g1\,\text{g}1g of substance,

m=1 g=10−3 kgm = 1\,\text{g} = 10^{-3}\,\text{kg}m=1g=10−3kg

Take

c=3×108 m/sc = 3 \times 10^8\,\text{m/s}c=3×108m/s

So,

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

E=10−3×9×1016E = 10^{-3} \times 9 \times 10^{16}E=10−3×9×1016

E=9×1013 JE = 9 \times 10^{13}\,\text{J}E=9×1013J

  1. Convert joules to electron volts.

We use

1 eV=1.6×10−19 J1\,\text{eV} = 1.6 \times 10^{-19}\,\text{J}1eV=1.6×10−19J

Hence,

E=9×10131.6×10−19 eVE = \frac{9 \times 10^{13}}{1.6 \times 10^{-19}}\,\text{eV}E=1.6×10−199×1013​eV

E=91.6×1032 eVE = \frac{9}{1.6} \times 10^{32}\,\text{eV}E=1.69​×1032eV

E=5.625×1032 eVE = 5.625 \times 10^{32}\,\text{eV}E=5.625×1032eV

  1. Convert eV to MeV.

Since

1 MeV=106 eV1\,\text{MeV} = 10^6\,\text{eV}1MeV=106eV

therefore,

E=5.625×1026 MeVE = 5.625 \times 10^{26}\,\text{MeV}E=5.625×1026MeV

E≈5.6×1026 MeVE \approx 5.6 \times 10^{26}\,\text{MeV}E≈5.6×1026MeV

  1. Match with the options.

Option A is:

5.6×1026 MeV5.6 \times 10^{26}\,\text{MeV}5.6×1026MeV

So the correct answer is A.

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