Question

The rest energy of an electron is $0.511MeV.$ The electron is accelerated from rest to a velocity $0.5c$. The change in its energy will be

• A. $0.026MeV$
• B. $0.051MeV$
• C. $0.07MeV$
• D. $0.105MV$

Answer 1

Answer: (C)

$0.07MeV$

$m{c}^2=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}{c}^2=\frac{m_0}{\sqrt{1-\frac{(0.5c{)}^2}{c^2}}}{c}^2$$=\frac{m_0}{\sqrt{1-0.25}}{c}^2=\frac{m_0}{\sqrt{0.75}}{c}^2=1.15m_0{c}^2$

Change in energy $=1.15m_0{c}^2-m_0{c}^2$
$=0.15\times 9.1\times {10}^{-31}\times (3\times {10}^8{)}^2$
$=12.285\times {10}^{-15}J$
$=\frac{12.285\times {10}^{-15}}{1.6\times {10}^{-13}}MeV$
$=0.07678MeV$