Question

What is the de Broglie wavelength of an electron traveling at 1.34 x 10 m/s? Express your answer to three significant figures and include the appropriate units. View Available Hints)

Answer 1

Given

velocity of electron = 1.34 $\times$ 10⁵ m/s

We know the de Broglie wave equation

$\lambda$ = h / p

Where

$\lambda$ = wavelength

h = plancks constant = 6.626 $\times$ 10^-34 J.s 6.626 $\times$ 10^-34 kg.m²/s

p = momentum

momentum (p) = mass $\times$ velocity

mass of electron = 9.109 $\times$ 10^-31 kg

then

Momentum = p = 9.109 $\times$ 10^-31 kg $\times$ 1.34 $\times$ 10⁵ m/s = 12.206 $\times$ 10^-26 km.m/s

now

$\lambda$ = h / p

= 6.626 $\times$ 10^-34 kg.m²/s / 12.206 $\times$ 10^-26 km.m/s

= 5.43 $\times$ 10^-9 m

So our answer is 5.43 $\times$ 10^-9 m