Answer
$\Delta v = 2.7~cm/s$
Work Step by Step
We can find $\gamma$:
$K = E_0~(\gamma-1) = 1.5~MeV$
$\gamma-1 = \frac{1.5~MeV}{E_0}$
$\gamma = 1+\frac{1.5~MeV}{E_0}$
$\gamma = 1+\frac{1.5~MeV}{20~eV}$
$\gamma = 75,001$
We can find $\beta$:
$\gamma = \frac{1}{\sqrt{1-\beta^2}}$
$\sqrt{1-\beta^2} = \frac{1}{\gamma}$
$1-\beta^2 = \frac{1}{\gamma^2}$
$\beta^2 = 1-\frac{1}{\gamma^2}$
$\beta = \sqrt{1-\frac{1}{\gamma^2}}$
$\beta = \sqrt{1-\frac{1}{75,001^2}}$
$\beta = 0.999999999911$
Then the speed of the electron neutrino is $0.999999999911~c$
We can find the difference between the speed of light and the speed of the electron neutrino:
$\Delta v = c - 0.999999999911~c$
$\Delta v = (0.000000000089)~(3.0\times 10^8~m/s)$
$\Delta v = 0.027~m/s$
$\Delta v = 2.7~cm/s$
