Question

Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is $1.6 \times 10^{6} ms^{-1}$, calculate de Broglie wavelength associated with this electron.

Answer 1

The wave nature of electron was first proposed by de-Broglie.

According to de-Broglie theory, all moving particles have wave nature.

From plank's quantum theory and Einstein's mass energy relationship,

$E\quad =\quad hv\quad =\quad \frac { hC }{ \lambda  } \quad$ ..........................(1)

$E\quad =\quad m{ c }^{ 2 }$ ..........................(2)

From (1) and (2)

$\frac { hc }{ \lambda  } \quad =\quad m{ c }^{ 2 }\quad or\quad \frac { h }{ \lambda  } \quad =\quad mc\quad or\quad \lambda \quad =\quad \frac { h }{ mc }$

Velocity of micro particle is “v” is,

$\lambda \quad =\quad \frac { h }{ mv } \quad =\quad \frac { h }{ P }$

From the given

$v\quad =\quad 1.6\quad \times \quad { 10 }^{ 6 }$

$\lambda \quad =\quad \frac { h }{ mv }$

$=\quad \frac { 6.626\quad \times \quad { 10 }^{ -34 } }{ (9.11\quad \times \quad { 10 }^{ -31 })(1.6\quad \times \quad { 10 }^{ 6 }) } \quad =\quad 4.55\quad \times \quad { 10 }^{ -10 }m\quad$

$\lambda \quad =\quad 455\quad pm$

Answer 2

Answer:The wave nature of electron was first proposed by de-Broglie.

According to de-Broglie theory, all moving particles have wave nature.

From plank's quantum theory and Einstein's mass energy relationship,

..........................(1)

..........................(2)

From (1) and (2)

Velocity of micro particle is “v” is,

From the given