What is the velocity of an electron that has a de Broglie wavelength of 529Å?

Note: I haven't done too many of these DeBroglie type questions, but since no one else has answered, I figured I'd post what I came up with.

529 Å = 5.29 x 10^-8 m

The letter m is used for two things: mass of electron and meters, depending on context.

m = mass (electron) = 9.11 x 10^-31 kg

h = Planck’s constant = 6.626 x 10^-34 J • s

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Find the energy of the electron:

λ = [h / √(2Em)]

√(2Em) = (h/λ)

2Em = (h/λ)²

E = [(h/λ)² / 2m]

= [(6.626 x 10^-34 J • s) / (5.29 x 10^-8 m)]² / (2 * 9.11 x 10^-31 kg)

= 8.611 x 10^-23 J

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Use the kinetic energy equation to find the velocity:

E = (1/2)mv²

v² = (2E / m)

v = √(2E / m)

= √{ [2 * (8.611 x 10^-23 J)] / (9.11 x 10^-31 kg) }

= 1.37 x 10^4 m/s ……… to 3 significant figures