Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 17: Problem 107

The inside of a cell membrane is at a potential of \(90.0 \mathrm{mV}\) lower than the outside. How much work does the electric field do when a sodium ion (Na') with a charge of \(+e\) moves through the membrane from outside to inside?

Short Answer

Expert verified
Answer: The work done by the electric field on a sodium ion is -1.44 x 10^-20 J.

Step by step solution

01

Identify the given quantities

We are given the following information: - Potential difference between inside and outside of the cell membrane (\(\Delta V\)): \(-90.0 \mathrm{mV}\) - Charge of a sodium ion (\(q\)): \(+e\)
02

Convert the potential difference to volts (V)

The potential difference value is given in millivolts (mV). Convert it to volts (V) by dividing by 1000: \(\Delta V = -90.0 \mathrm{mV} \times \frac{1 \mathrm{V}}{1000 \mathrm{mV}} = -0.090 \mathrm{V}\)
03

Calculate the work done by the electric field

Use the formula for work done by an electric field, \(W=q\Delta V\), where \(q\) is the charge of the sodium ion and \(\Delta V\) is the potential difference: \(W = (+e)(-0.090 \mathrm{V})\) Here, \(e\) represents the elementary charge, which is approximately \(1.6 \times 10^{-19} \mathrm{C}\). Substitute this value into the equation: \(W = (1.6 \times 10^{-19}\mathrm{C})(-0.090 \mathrm{V})\)
04

Calculate the final answer

Multiply the values to get the work done by the electric field: \(W = -1.44 \times 10^{-20} \mathrm{J}\) The electric field does \(-1.44 \times 10^{-20} \mathrm{J}\) of work on the sodium ion as it moves through the cell membrane from outside to inside. The negative sign indicates that the work is done against the electric force, which means that the work is done on the sodium ion.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

To make a parallel plate capacitor, you have available two flat plates of aluminum (area \(120 \mathrm{cm}^{2}\) ), a sheet of paper (thickness $=0.10 \mathrm{mm}, \kappa=3.5),\( a sheet of glass (thickness \)=2.0 \mathrm{mm}, \kappa=7.0),\( and a slab of paraffin (thickness \)=10.0 \mathrm{mm}, \kappa=2.0) .$ (a) What is the largest capacitance possible using one of these dielectrics? (b) What is the smallest?
A parallel plate capacitor has a capacitance of \(1.20 \mathrm{nF}\) There is a charge of magnitude \(0.800 \mu\) C on each plate. (a) What is the potential difference between the plates? (b) If the plate separation is doubled, while the charge is kept constant, what will happen to the potential difference?
If an electron moves from one point at a potential of \(-100.0 \mathrm{V}\) to another point at a potential of \(+100.0 \mathrm{V}\) how much work is done by the electric field?
The bottom of a thundercloud is at a potential of $-1.00 \times 10^{8} \mathrm{V}\( with respect to Earth's surface. If a charge of \)-25.0 \mathrm{C}$ is transferred to the Earth during a lightning strike, find the electric potential energy released. (Assume that the system acts like a capacitor-as charge flows, the potential difference decreases to zero.)
A large parallel plate capacitor has plate separation of \(1.00 \mathrm{cm}\) and plate area of \(314 \mathrm{cm}^{2} .\) The capacitor is connected across a voltage of \(20.0 \mathrm{V}\) and has air between the plates. How much work is done on the capacitor as the plate separation is increased to $2.00 \mathrm{cm} ?$
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Waves Physics

Read Explanation

Work Energy and Power

Read Explanation

Electrostatics

Read Explanation

Physical Quantities And Units

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free