Work Done = Change in Kinetic Energy The work needed is the same as how much the electron's kinetic energy increases. At the start, the electron is at rest, so its initial kinetic energy KEi=0. After speeding up, the electron's final kinetic energy KEf=W, where W is the work done. So, W=KEf−KEi=KEf=W Relating de-Broglie Wavelength to Kinetic Energy The de-Broglie wavelength formula is: λd=‌
h
mv
=‌
h
p
For an electron (or any particle), p=√2mKE. So, λd=‌
h
√2mKE
From above, KE=W (work done). Therefore, λd=‌
h
√2mW
Now, solve for W:λd2=‌
h2
2mW
W=‌
h2
λd2⋅2m
Plugging in the Numbers Given: Planck's constant, h=6.6×10−34Js
Mass of electron, m=9×10−31kg de-Broglie wavelength, λd=6600Å=6.6×10−7m So, W=‌
(6.6×10−34)2
(6.6×10−7)2×2×9.0×10−31
J Now calculate each step: Top: (6.6×10−34)2=43.56×10−68 Bottom: (6.6×10−7)2×2×9.0×10−31=(43.56×10−14)×18.0×10−31=784.08×10−45 So, W=‌