If a proton and an electron are released when they are 2.0×10−102.0\$$times10^{-10} m $$apart (a typical atomic distance), find the initial acceleration of each particle.

Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 15th Edition

Ch 21: Electric Charge and Electric Field

Problem 3

Chapter 21, Problem 3

If a proton and an electron are released when they are $2.0 \times 10^{- 10}$ m apart (a typical atomic distance), find the initial acceleration of each particle.

Verified step by step guidance

Start by identifying the forces acting on the proton and electron. The primary force here is the electrostatic force due to their charges. Use Coulomb's Law to calculate this force:

F = \frac{k q q}{r^{2}}

, where

k

is Coulomb's constant,

q

is the charge of the proton or electron, and

r

is the distance between them.

Calculate the electrostatic force using the known values:

k

= 8.99 × 10⁹ N m²/C²,

q

= 1.6 × 10^-19 C, and

r

= 2.0 × 10^-10 m.

Once the force is calculated, use Newton's second law to find the acceleration of each particle. Newton's second law states:

F = m a

, where

m

is the mass of the particle and

a

is the acceleration.

Calculate the acceleration of the proton using its mass:

m

= 1.67 × 10^-27 kg. Rearrange Newton's second law to solve for acceleration:

a = \frac{F}{m}

Similarly, calculate the acceleration of the electron using its mass:

m

= 9.11 × 10^-31 kg. Use the same rearranged formula:

a = \frac{F}{m}

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the force acting on the proton and electron due to their charges.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). This principle is crucial for determining the initial acceleration of the proton and electron once the electrostatic force is known.

Mass of Proton and Electron

Understanding the mass of the proton and electron is vital for calculating their acceleration. The proton has a mass of approximately 1.67 x 10^-27 kg, while the electron's mass is about 9.11 x 10^-31 kg. These values are necessary to apply Newton's Second Law and find the acceleration of each particle.

Recommended video:

Guided course

20:32

Mass Spectrometers

Related Practice

Textbook Question

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. How many electrons does each sphere contain? (The atomic mass of aluminum is $26.982$ g/mol, and its atomic number is $13$ .)

views

Textbook Question

Two small spheres spaced $20.0$ cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is $3.33 \times 10^{- 21}$ N?

views

Textbook Question

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about $20 comma 000$ C/s; this lasts for $100$ ms or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

views

Textbook Question

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude $1.00 \times 10^{4}$ N (roughly $1$ ton)? Assume that the spheres may be treated as point charges.

If a proton and an electron are released when they are 2.0×10−102.0\(\times\)10^{-10} m apart (a typical atomic distance), find the initial acceleration of each particle.

Verified video answer for a similar problem:

Key Concepts

Coulomb's Law

Newton's Second Law of Motion

Mass of Proton and Electron

If a proton and an electron are released when they are $2.0 \times 10^{- 10}$ m apart (a typical atomic distance), find the initial acceleration of each particle.