Suggested languages for you:

Americas

Europe

Q17E

Expert-verifiedFound in: Page 134

Book edition
2nd Edition

Author(s)
Randy Harris

Pages
633 pages

ISBN
9780805303087

**Determine the Compton wavelength of the electron, defined to be the wavelength it would have if its momentum were${{\mathbf{\text{m}}}}_{{\mathbf{\text{e}}}}{\mathbf{\text{c}}}$**.

Compton Wavelength of the electron

$\lambda =\text{2.43}\times {\text{10}}^{\text{-12}}\text{m}$

${\text{m}}_{\text{e}}{\text{=9.1\xd710}}^{\text{-31}}\text{kg --}$ the electron's mass

${\text{p=m}}_{\text{e}}\text{c --}$ the electron's momentum

**The following equation can be used to describe the de Broglie wavelength.**

**${\mathbf{\text{p=}}}\frac{\mathbf{\text{h}}}{\mathbf{\text{\lambda}}}$…………………..(1)**

Know that the electron's momentum is${\text{p=m}}_{\text{e}}\text{c}$ .

Get the wavelength expression as follows

$\text{p=}\frac{\text{h}}{\text{\lambda}}$

${\text{p=m}}_{\text{e}}\text{c}$

${\text{m}}_{\text{e}}\text{c=}\frac{\text{h}}{\text{\lambda}}$

$\text{\lambda =}\frac{\text{h}}{{\text{m}}_{\text{e}}\text{c}}$

Using the wavelength's derived expression, Obtain$\lambda $ as:

$\begin{array}{c}\lambda =\frac{\text{h}}{{\text{m}}_{\text{e}}\text{c}}\\ =\frac{\text{6.626}\times {\text{10}}^{\text{-34}}\text{\hspace{0.17em}}J\cdot s}{(\text{9.1}\times {\text{10}}^{\text{-31}}\text{\hspace{0.17em}}kg)\times (\text{3.0}\times {\text{10}}^{\text{8}}\text{\hspace{0.17em}}m/s)}\\ =\text{2.43}\times {\text{10}}^{\text{-12}}\text{m}\end{array}$ $\begin{array}{c}\lambda =\frac{\text{h}}{{\text{m}}_{\text{e}}\text{c}}\\ =\frac{\text{6.626}\times {\text{10}}^{\text{-34}}\text{\hspace{0.17em}}J\cdot s}{(\text{9.1}\times {\text{10}}^{\text{-31}}\text{\hspace{0.17em}}kg)\times (\text{3.0}\times {\text{10}}^{\text{8}}\text{\hspace{0.17em}}m/s)}\\ =\text{2.43}\times {\text{10}}^{\text{-12}}\text{m}\end{array}$

The Compton Wavelength of the electron is$\lambda =\text{2.43}\times {\text{10}}^{\text{-12}}\text{m}$ .

94% of StudySmarter users get better grades.

Sign up for free