Answer
The change in velocity is $0.078~m/s$
Work Step by Step
We can use the kinetic energy $E$ to write an expression for the speed of a particle:
$E = \frac{1}{2}mv^2$
$v = \sqrt{\frac{2~E}{m}}$
We can find the speed of the particle when it absorbs a photon with a wavelength of $660~nm$:
$v = \sqrt{\frac{2~E}{m}}$
$v = \sqrt{\frac{2~(\frac{hc}{\lambda})}{m}}$
$v = \sqrt{\frac{2~h~c}{m~\lambda}}$
$v = \sqrt{\frac{(2)(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{(1.0\times 10^{-16}~kg)(660\times 10^{-9}~m)}}$
$v = 0.078~m/s$
The change in velocity is $0.078~m/s$
