Question on the de Broglie wavelength for an electron.?

Question

What is the de Broglie wavelength for an electron with speed a) v = 0.480c and b) v = 0.960c? (Hint: Use the correct relativistic expression for linear momentum if necessary.) They are using p = mc times square root of (gamma-squared -1). What is the value of gamma/gamma-squared here? Is it a constant? For a), they wrote "λ = h/p = (h/mc) / (square root of (gamma squared -1)) = 4.43 x 10^(-12) m. I don't understand why we can't just simply use λ = h/p, which is the nonrelativistic equation.

Answer 1

(a)

v = 0.480c = 0.480*3*(10^8) = 144*(10^6) m\s

use λ = h \ γmv  

where λ is wavelength

m is rest mass of electron = 9,1*10^ -31kg

v is the electron velocity

γ (gamma) is Lorenz factor = 1 \ sqrt( 1 - v^2\c^2 )

do it on your calculator this is the way I always use

Answer 2

λ = h/p is correct no matter what.

For a nonrelativistic particle, p = mv.

For a relativistic particle,

p = gamma mv

= mv / sqrt (1 - (v/c)^2)

Marwa--for God's sake--don't convert v to m/s.  The speed only shows up in the ratio of v/c, so if they give you v = something times c, then v/c is just that something.

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You are correct, the non-relativistic equation does not get the right answer.  The non-relativistic equation is wrong.  The non-relativistic equation only works when v/c is small and gamma is not significantly greater than one.