Question

A protein molecule in an electrophoresis gel has a negative charge.The exact charge depends on the pH of the solution, but 30 excess electrons is typical.

a) What is the magnitude of the electric forceon a protein with this charge in a 1500 N/C electric field? (I understand this part, answer: 7.2 x 10^-15 N)

b) When released from the rest, does the charged protien molecule move parallel to the electric field or opposite to the electric field? (I think opposite to the electric field, is that correct?)

c) What is the acceleration of the protein molecule? Assume the mass of protein is 9.20 x 10^-20 kg.

d) Assuming the acceleration is constant, how does it take the protein molecule to travel 10.0 cm. The molecule starts from rest.

Answer 1

Part a

Total charge =

$30\times 1.6\times 10^{-19}C=48\times 10^{-19} C$

The electric field is

Therefore, the electric force magnitude $=1500\times 48\times 10^{-19} N$

$=7.2\times 10^{-15} N$ (same as your result)

Part b

An electron is negatively charged. Therefore, the charged protein molecule will move in a direction opposite to the electric field.

Part c

The force is $=7.2\times 10^{-15} N$ . The given mass is $=9.20\times 10^{-20} kg$

The acceleration $=\frac{7.2\times 10^{-15}}{9.20\times 10^{-20}} m/s^{2}=7.82\times 10^{4}m/s^{2}$

Part d

If the molecule starts from rest, the time taken can be calculated from the equation $S=\frac{1}{2}at^{2}$

Given:

Therefore, $t^{2}=\frac{2S}{a}$

$t^{2}=\frac{2\times 0.1}{7.82\times 10^{4}} s^{2}$

$t^{2}=0.025\times 10^{-4} s^{2}$

$t=0.16\times 10^{-2} s$   , this is the required time.