Question

what is the wavelength, in pm, of an electron when its velocity is 66.67% the speed of light?

Answer 1

as we know the de brogile wavelength equation as lamda = plancks constant/momentum

λ = h/m*v

velocity of light is 3x 10⁸ m/s² ; h = 6.636 * 10^-34 J.s

66.67% of speed of light= 66.67/100 * [3*10⁸] = 2 *10⁸

Mass of an electron =9.1 ×10^-31kg

λ = 6.636*10-34 / 9.1*10-31 *(2*108)

we get lambda= 3.646 * 10^-12 m

we also know that 1 m = 10¹² pm

3.646 * 10^-12 m = 3.646 * 10^-12 x 10¹² = 3.646 pm

hence the final answer must be 3.646 pm

Hope this helped you!

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