Homework Help Forum: Physics
Posted by Sandra on Sunday, February 28, 2010 at 10:20am.
Thank you for answering my previous questions!
I have another one now in regards to the following question...
An unknown potential difference exists between the inner and outer surfaces of the membrane of a cell. The inner surface is negative relative to the outer surface. If 1.7 x 10-20 J of work is needed to eject a positive Calcium ion (Ca2+) from the interior of the cell, what is the value of the potential difference?
I think that I should be able to use the formula where work is equal to the charge of the particle times its electric potential difference. The work is given and by using the charge of the calcium ion, the electric potential difference could easily be solved for. However, my question is, what would the charge of the calcium ion be? Do we need to consider it's electrons/protons? Since it's given that it charge is 2+, would I just assume that its 2X the charge of a proton?
Thanks in advance!
* Physics - Sandra, Sunday, February 28, 2010 at 7:18pm
If someone can help, I'd really appreciate it!
Yes, that is how to do it. The charge of Ca(2+) is +2e, or 3.2*16^-19 C
To find the value of the potential difference, you can use the formula:
Work = charge of the particle x electric potential difference.
In this case, the work is given as 1.7 x 10^-20 J.
The charge of the calcium ion (Ca2+) is 2+. This means it has a charge of +2, which is 2 times the charge of a proton.
To understand why the charge is 2+, you need to consider the atomic structure of calcium. Calcium has an atomic number of 20, which means it has 20 protons in its nucleus. In a neutral calcium atom, there would be an equal number of electrons orbiting the nucleus. However, in a calcium ion with a charge of 2+, it has lost 2 electrons. Since electrons have a negative charge, when an atom loses electrons, it becomes positively charged. So a calcium ion with a charge of 2+ has 18 electrons (-18) and 20 protons (+20), resulting in a net charge of +2.
Therefore, you can indeed assume that the charge of the calcium ion is 2 times the charge of a proton.
By substituting the given values into the formula, you can now solve for the potential difference:
1.7 x 10^-20 J = (charge of calcium ion) x (electric potential difference)
1.7 x 10^-20 J = (2e) x (electric potential difference)
where e is the elementary charge, which is approximately 1.6 x 10^-19 C.
You can now rearrange the equation to solve for the electric potential difference:
electric potential difference = (1.7 x 10^-20 J) / (2e)
Please calculate this expression to find the value of the potential difference between the inner and outer surfaces of the cell's membrane.