Question

Calculate the wavelength of an electron if its kinetic energy is $3.0\times {10}^{-25}J$. Mass of an electron is $9.1\times {10}^{-31}Kg$ :

• A. $7.82\times {10}^{-7}m$
• B. $8.99\times {10}^{-7}m$
• C. $0.89\times {10}^{-7}m$
• D. $9.67\times {10}^{-7}m$

Answer 1

Answer: (B)

$8.99\times {10}^{-7}m$

Given:

mass of an electron = $9.1\times {10}^{-31}$kg

kinetic energy = $3.0\times {10}^{-25}$ J

h = $6.6\times {10}^{-34}$ Js

By using de- Broglie equation :

$\lambda$= $\frac{h}{mv}$ = $\frac{h}{p}$ ,where h = Planck's constant, p= momentum

as P = $\sqrt{2\times E\times m}$ , by subtituting the value of p we get,

wavelength = $\frac{h}{\sqrt{2\times E\times m}}$ (E= kinetic energy )

wavelength = $\frac{6.6\times {10}^{-34}}{\sqrt{2\times 3\times {10}^{-25}\times 9.1\times {10}^{-31}}}$

= $0.89\times {10}^{-6}$ m