Class 11 Exam > Class 11 Questions > Calculate the distance of closest approach be...
Start Learning for Free
Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C?
Most Upvoted Answer
Calculate the distance of closest approach between an alpha particle o...
Given:
Energy of the alpha particle (E) = 5.5 MeV = 5.5 × 10^6 × 1.6 × 10^-19 J
Charge on the gold nucleus (Q) = 79e = 79 × 1.6 × 10^-19 C
Charge on the alpha particle (q) = 2e = 2 × 1.6 × 10^-19 C
To find:
Distance of closest approach between the alpha particle and the gold nucleus.
Formula:
The distance of closest approach (r) can be calculated using the Coulomb's law:
E = (Qq)/(4πε₀r)
Where:
E = Energy of the alpha particle
Q = Charge on the gold nucleus
q = Charge on the alpha particle
ε₀ = Permittivity of free space
r = Distance of closest approach
Solution:
Step 1: Convert the energy of the alpha particle from MeV to joules:
5.5 MeV = 5.5 × 10^6 × 1.6 × 10^-19 J
Step 2: Substitute the given values into the formula:
5.5 × 10^6 × 1.6 × 10^-19 J = (79 × 1.6 × 10^-19 C × 2 × 1.6 × 10^-19 C)/(4πε₀r)
Step 3: Simplify the equation:
5.5 × 10^6 × 1.6 × 10^-19 J = (79 × 1.6 × 10^-19 C × 2 × 1.6 × 10^-19 C)/(4πε₀r)
Step 4: Cancel out common terms:
5.5 × 10^6 = 79 × 2/(4πε₀r)
Step 5: Rearrange the equation to solve for r:
r = (79 × 2)/(5.5 × 10^6 × 4πε₀)
Step 6: Substitute the values of ε₀ and π:
ε₀ = 8.854 × 10^-12 C^2/(N·m^2)
π ≈ 3.14159
Step 7: Calculate the value of r:
r = (79 × 2)/(5.5 × 10^6 × 4 × 3.14159 × 8.854 × 10^-12) m
Step 8: Simplify the expression:
r ≈ 1.44 × 10^-14 m
Answer:
The distance of closest approach between the alpha particle and the gold nucleus is approximately 1.44 × 10^-14 meters.
Energy of the alpha particle (E) = 5.5 MeV = 5.5 × 10^6 × 1.6 × 10^-19 J
Charge on the gold nucleus (Q) = 79e = 79 × 1.6 × 10^-19 C
Charge on the alpha particle (q) = 2e = 2 × 1.6 × 10^-19 C
To find:
Distance of closest approach between the alpha particle and the gold nucleus.
Formula:
The distance of closest approach (r) can be calculated using the Coulomb's law:
E = (Qq)/(4πε₀r)
Where:
E = Energy of the alpha particle
Q = Charge on the gold nucleus
q = Charge on the alpha particle
ε₀ = Permittivity of free space
r = Distance of closest approach
Solution:
Step 1: Convert the energy of the alpha particle from MeV to joules:
5.5 MeV = 5.5 × 10^6 × 1.6 × 10^-19 J
Step 2: Substitute the given values into the formula:
5.5 × 10^6 × 1.6 × 10^-19 J = (79 × 1.6 × 10^-19 C × 2 × 1.6 × 10^-19 C)/(4πε₀r)
Step 3: Simplify the equation:
5.5 × 10^6 × 1.6 × 10^-19 J = (79 × 1.6 × 10^-19 C × 2 × 1.6 × 10^-19 C)/(4πε₀r)
Step 4: Cancel out common terms:
5.5 × 10^6 = 79 × 2/(4πε₀r)
Step 5: Rearrange the equation to solve for r:
r = (79 × 2)/(5.5 × 10^6 × 4πε₀)
Step 6: Substitute the values of ε₀ and π:
ε₀ = 8.854 × 10^-12 C^2/(N·m^2)
π ≈ 3.14159
Step 7: Calculate the value of r:
r = (79 × 2)/(5.5 × 10^6 × 4 × 3.14159 × 8.854 × 10^-12) m
Step 8: Simplify the expression:
r ≈ 1.44 × 10^-14 m
Answer:
The distance of closest approach between the alpha particle and the gold nucleus is approximately 1.44 × 10^-14 meters.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C?
Question Description
Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C?.
Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C?.
Solutions for Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? defined & explained in the simplest way possible. Besides giving the explanation of
Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C?, a detailed solution for Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? has been provided alongside types of Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? theory, EduRev gives you an
ample number of questions to practice Calculate the distance of closest approach between an alpha particle of energy 5.5 MeV (5.5 × 10^6 × 1.6 × 10^-19) if the charge on the gold nucleus is 79e = 79 × 1.6 × 10^-19 C and the charge on the alpha particle is 2e = 2 × 1.6 × 10^-19 C? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup