Answer
a. $\lambda= 4.43\times10^{-12}m$.
b. $\lambda= 7.07\times10^{-13}m$.
Work Step by Step
From section 37.7, equation 37.27, the relativistic momentum is $p=\frac{mv}{\sqrt{1-v^2/c^2}}$.
a. $\lambda=\frac{h}{p}=\frac{h\sqrt{1-v^2/c^2}}{mv}$
$\lambda=\frac{(6.626\times10^{-34}J \cdot s)\sqrt{1-0.480^2}}{(9.11\times10^{-31}kg)(0.480)(3.00\times10^{8}m/s)}$
$\lambda= 4.43\times10^{-12}m$
b. $\lambda=\frac{h}{p}=\frac{h\sqrt{1-v^2/c^2}}{mv}$
$\lambda=\frac{(6.626\times10^{-34}J \cdot s)\sqrt{1-0.960^2}}{(9.11\times10^{-31}kg)(0.960)(3.00\times10^{8}m/s)}$
$\lambda= 7.07\times10^{-13}m$
