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Convert $1 u$ of mass in $eV$ energy. $(1 u = 1.66 \times 10^{- 27} kg)$

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931.5 \times 10^{5} eV

931.5 \times 10^{9} eV

931.5 \times 10^{6} eV

931.5 \times 10^{3} eV

answer is A.

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Detailed Solution

The 1 u of mass into eV energy is given by

931.5 \times 10^{5} eV

According to Einstein, mass energy equivalence

E = m c^{2}

Where,

m = mass

C = speed of light

E = Energy

Where,

m = 1.66 \times 10^{- 27} kg

C = 3 \times 10^{8} m / \sec

E = 1 \times (3 \times 10^{8})^{2}

E = 9 \times 10^{16} u m^{2} / s^{2}

1 u = 1.6605 \times 10^{- 27} kg

E = 1.6605 \times 10^{- 27} \times 9 \times 10^{16}

= 1.4924 \times 10^{- 10}

Convert it into eV
=

\frac{1.4924 \times 10^{- 10}}{1.602 \times 10^{- 19}}

= 0.9315 eH \times 10^{3}

E = 931.5 \times 10^{6} eV

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