An alternating current of frequency f=8.5 MHzf = 8.5\text{ MHz}f=8.5 MHz is passed through a microfluidic channel containing sodium ions (Na+\text{Na}^+Na+). Within the channel, the magnitude of the maximum alternating current is 4.5 μA4.5\text{ }\mu\text{A}4.5 μA. The channel has a cross-sectional area of 1.2×10−9 m21.2 \times 10^{-9}\text{ m}^21.2×10−9 m2 and the sodium ion carrier number density is 5.0×1025 m−35.0 \times 10^{25}\text{ m}^{-3}5.0×1025 m−3. Take the charge of a sodium ion to be 1.6×10−19 C1.6 \times 10^{-19}\text{ C}1.6×10−19 C.
Show that the maximum drift velocity of each sodium ion in the channel is approximately 4.7×10−4 m s−14.7 \times 10^{-4}\text{ m s}^{-1}4.7×10−4 m s−1.
The motion of the sodium ions is modeled as simple harmonic motion. Use the drift velocity from (i) to calculate the amplitude AAA of this motion.
Without further calculation, explain how the maximum acceleration of a sodium ion varies as the frequency fff is adjusted, provided that the maximum alternating current remains constant.
