Question

Find the kinetic energy of an electron whose de broglie wavelength is the same as a 100 kev x ray

Answer 1

Answer :

$9.34 {10}^{ - 10} joules$

Explanation: Refer to the material.

Answer 2

Solution:

kinetic energy of an electron: $9.34* 10^{-10} J$

Explanation:

As we know from formula λ$=\frac{h}{p}$ $= \frac{h}{\sqrt{2mk} }$

here, P$= {\sqrt{2mk} }$

given,  λ= 100kev  

putting in equation,

$100* 10^{3}*1.6*10^{-19} = \frac{6.6*10^{-34} }{\sqrt{2*9.1*10^{-31} k} }$

$(100* 10^{3}*1.6*10^{-19})^{2} = (\frac{6.6*10^{-34} }{\sqrt{2*9.1*10^{-31} k} })^{2}$

$k = \frac{ (\frac{6.6*10^{-34} }{\sqrt{2*9.1*10^{-31} } })^{2}}{(100* 10^{3}*1.6*10^{-19})^{2}}$

by calculation the value of kinetic energy will be :

$k= 9.34*10^{-10} J$