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Question: Answered & Verified by Expert
As per Einstein's theory, energy equivalent of $1 \mathrm{gm}$ (One gram) substance will be
PhysicsNuclear PhysicsJEE Main
Options:
  • A $5.6 \times 10^{26} \mathrm{MeV}$
  • B $9.09 \times 10^{13} \mathrm{MeV}$
  • C $5.6 \times 10^{29} \mathrm{MeV}$
  • D $5.6 \times 10^{32} \mathrm{MeV}$
Solution:
2170 Upvotes Verified Answer
The correct answer is: $5.6 \times 10^{26} \mathrm{MeV}$
Given, mass $\mathrm{m}=1 \mathrm{gm}=10^{-3} \mathrm{~kg}$
speed of light $\mathrm{c}=3 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$
Energy $E=\mathrm{mc}^2=\left(10^{-3} \mathrm{~kg}\right)\left(3 \times 10^8 \mathrm{~ms}^{-1}\right)^2=9 \times 10^{13}$ Joule
1 electron volt $=1.602 \times 10^{-19}$ Joule
So the given energy is $=6.242 \times 10^{18} \times 9 \times 10^{13} \mathrm{eV}$
Converting it in $\mathrm{MeV}$, we need to divide it by $10^{-3}$
The answer will be approx $5.6 \times 10^{26} \mathrm{Mev}$

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