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Question: A electron of rest mass \(1.67 \times 10^{- 27}\) kg is moving with a velocity of 0.9c (c = velocity...

A electron of rest mass 1.67×10−271.67 \times 10^{- 27} kg is moving with a velocity of 0.9c (c = velocity of light). Find its mass and momentum.

A

10.34×10−1910.34 \times 10^{- 19}

B

8.01×10108.01 \times 10^{10}

C

9.652×10−189.652 \times 10^{- 18}

D

None

Answer

10.34×10−1910.34 \times 10^{- 19}

Explanation

Solution

Mass of a moving object can be calculated using Einsten’s theory of relativity :

m′=m1−(u/c)2m^{'} = \frac{m}{\sqrt{1 - (u/c)^{2}}} m=m = rest mass (given), u = velocity (given), c = velocity of light

m′=1.67×10−271−(0.9cc)2=3.83×10−27kgm^{'} = \frac{1.67 \times 10^{- 27}}{\sqrt{1 - \left( \frac{0.9c}{c} \right)^{2}}} = 3.83 \times 10^{- 27}kg

Momentum ′p′=m′×u'p' = m^{'} \times u

p=3.83×10−27×0.9c=10.34×10−19kgms−1\mathbf{p = 3.83}\mathbf{\times}\mathbf{1}\mathbf{0}^{\mathbf{-}\mathbf{27}}\mathbf{\times}\mathbf{0.9c = 10.34}\mathbf{\times}\mathbf{1}\mathbf{0}^{\mathbf{-}\mathbf{19}}\mathbf{kgm}\mathbf{s}^{\mathbf{-}\mathbf{1}}