Question

Out of a photon and an electron, the equation $$E = Pc$$, is valid for

A
both
B
neither
C
photon only
D
electron only

Solution

The correct option is C photon onlyEnergy is given by$$E=\dfrac { { m }_{ 0 }{ c }^{ 2 } }{ \sqrt { 1-\dfrac { { v }^{ 2 } }{ { c }^{ 2 } } } }$$$$\Rightarrow { E }^{ 2 }=\dfrac { { m }_{ 0 }^{ 2 }{ c }^{ 6 } }{ { c }^{ 2 }-{ v }^{ 2 } }$$Momentum $$P$$ is given by$$P=\dfrac { { m }_{ 0 }v }{ \sqrt { 1-\left( \dfrac { { v }^{ 2 } }{ { c }^{ 2 } } \right) } }$$$${ P }^{ 2 }{ c }^{ 2 }=\dfrac { { m }_{ 0 }^{ 2 }{ c }^{ 4 }{ v }^{ 2 } }{ { c }^{ 2 }-{ v }^{ 2 } }$$$$\therefore { E }^{ 2 }-{ P }^{ 2 }{ c }^{ 2 }={ m }_{ 0 }^{ 2 }{ c }^{ 4 }$$$$\Rightarrow { E }^{ 2 }={ P }^{ 2 }{ c }^{ 2 }+{ m }_{ 0 }^{ 2 }{ c }^{ 4 }$$For photon, rest mass$${ m }_{ 0 }=0$$, so $$E=Pc$$For electron, $${ m }_{ 0 }\neq 0$$, so $$E\neq Pc$$PhysicsNCERTStandard XII

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