(adsbygoogle = window.adsbygoogle || []).push({}); De broglie wavelength of fast moving particle--help please!

1. The problem statement, all variables and given/known data

A particle moving with kinetic energy equal to its rest energy has a de Broglie wavelength of 1.7898 *10^-16 m. If the kinetic energy doubles, what is the new de Broglie wavelength?

2. Relevant equations

λ=h/√(2mK)

m=m_{0}γ

K=E_{t}-E_{0}

3. The attempt at a solution

Initially:

K=m_{0}c^{2}=E_{T}-m_{0}c^{2}

But E_{T}=m_{0}c^{2}γ

thus: 2=γ, which implies v=1/2(√3)

λ=h/√(2mK)=h/√2m_{0}γ*m_{0}c^{2}=

h/(2m_{0}c)

Then when the K becomes twice the rest mass:

K=E_{t}-E_{0}

3m_{0}c^{2}=m_{0}c^{2}γ, which implies γ=3

so λ=h/√(2m_{0}γK)=h/√2m_{0}*3*(2m_{0}c^{2}

=h/(2m_{0}c*√3), which is just the original λ divided by the root of 3.

1.7898/√3= 1.03, so λ=1.033*10^-16, but the answer is λ=1.096*10^-16

Please help-- I have been wracking my brains about this for two days!

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# Homework Help: De broglie wavelength of fast moving particle-help please!

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