Question

The mass of an electron is $9.1 \times 10^{-31}$ kg. If its K.E. is $3.0 \times 10^{-25} J$, calculate its wavelength.

Answer 1

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Answer 2

"A particle's de-Broglie wavelength is defined as Planck's constant divided by the particle's momentum

$Kinetic\quad energy\quad of\quad electron\quad =\quad \frac { 1 }{ 2 } m{ v }^{ 2 }$

$=\sqrt { \frac { 2\quad \times \quad 3.0\quad \times \quad { 10 }^{ -25 }\quad J }{ 9.11\quad \times \quad { 10 }^{ -31 }\quad kg }  }$

From the above,

$v\quad =\quad \frac { \sqrt { 2 } K.E }{ m } =\quad 812\quad m{ s }^{ -1 }$

By de-Broglie equation,

$\lambda\quad =\quad \frac { h }{ mv } =\quad \frac { 6.626\quad \times \quad { 10 }^{ -34 }Js }{ (9.11\quad \times \quad { 10 }^{ -31 }\quad Kg)(812) } \quad =\quad 8.967\quad \times \quad { 10 }^{ -7 }\quad m$

Therefore, wavelength of electron is $8.967\quad \times \quad { 10 }^{ -7 }$ m"