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Physics Question on Modern Physics

The energy equivalent of 1g of substance is:

A

11.2×1024 MeV11.2 \times 10^{24} \, \text{MeV}

B

5.6×1012 MeV5.6 \times 10^{12} \, \text{MeV}

C

5.6 eV5.6 \, \text{eV}

D

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

Answer

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

Explanation

Solution

The energy equivalent of a mass is given by Einstein’s equation:

E=mc2,E = mc^2,

where:

  • m=1 g=10−3 kg,m = 1 \, \text{g} = 10^{-3} \, \text{kg},
  • c=3×108 m/s.c = 3 \times 10^8 \, \text{m/s}.

Step 1: Substitute values into E=mc2E = mc^2

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

Simplify:

E=(10−3)×(9×1016) J.E = (10^{-3}) \times (9 \times 10^{16}) \, \text{J}.

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

Step 2: Convert energy to electron volts (eV)

Using the conversion 1 J=6.241×1018 eV:1 \, \text{J} = 6.241 \times 10^{18} \, \text{eV}:

E=(9×1013)×(6.241×1018) eV.E = (9 \times 10^{13}) \times (6.241 \times 10^{18}) \, \text{eV}.

E=56.169×1031 eV.E = 56.169 \times 10^{31} \, \text{eV}.

Convert to MeV (1 MeV=106 eV1 \, \text{MeV} = 10^6 \, \text{eV}):

E=56.169×1025 MeV.E = 56.169 \times 10^{25} \, \text{MeV}.

Approximate:

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

Final Answer: 5.6×1026 MeV.5.6 \times 10^{26} \, \text{MeV}.