For most large spherical nuclei, the radius can be estimated by the equation r = r0A1/3, where r0 = 1.15E-15 m. What is the radius of a large spherical nucleus with a mass number A = 123? r =  m. What is the minimum possible electric force between two protons in this nucleus? F =  N.


Let's break down the problem into two parts:

1. **Calculate the radius \( r \) of the nucleus:**

The formula for the radius of a large spherical nucleus is given as:
\[
r = r_0 A^{1/3}
\]
Where:
- \( r_0 = 1.15 \times 10^{-15} \, \text{m} \)
- \( A = 123 \) (mass number of the nucleus)

Now we can substitute these values and solve for \( r \).

\[
r = 1.15 \times 10^{-15} \times 123^{1/3} \, \text{m}
\]

2. **Calculate the minimum possible electric force between two protons:**

The electric force between two protons can be estimated using Coulomb's law:
\[
F = \frac{k_e q_1 q_2}{r^2}
\]
Where:
- \( k_e = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \) (Coulomb's constant)
- \( q_1 = q_2 = 1.602 \times 10^{-19} \, \text{C} \) (charge of a proton)
- \( r \) is the distance between the two protons, which can be approximated as the nuclear radius.

We can now substitute the values of \( q_1 \), \( q_2 \), and \( r \) to calculate the electric force \( F \).

Let me calculate both parts now.1. The radius \( r \) of the nucleus is approximately \( 5.72 \times 10^{-15} \, \text{m} \).

2. The minimum possible electric force between two protons in this nucleus is approximately \( 7.05 \, \text{N} \).

Would you like more details or have any further questions? 

Here are 5 related questions you might find interesting:
1. How does the radius of a nucleus change with a different mass number \( A \)?
2. What are the factors affecting the electric force between protons in a nucleus?
3. How would the electric force change if the protons were further apart than the nuclear radius?
4. Can we use the same formula to estimate the force between neutrons in the nucleus?
5. What is the role of nuclear forces in keeping the nucleus stable despite this repulsive electric force?

**Tip:** The nuclear radius grows proportionally to \( A^{1/3} \), meaning larger nuclei only grow slightly bigger despite containing many more nucleons.

For most large spherical nuclei, the radius can be estimated by the equation r = r0A^(1/3), where r0 = 1.15E-15 m. What is the radius of a large spherical nucleus with a mass number A = 123? r =  m. What is the minimum possible electric force between two protons in this nucleus? F =  N.

Learn how to calculate the radius of a large spherical nucleus with mass number A = 123 using the formula r = r0 * A^(1/3). Additionally, determine the minimum possible electric force between two protons in the nucleus using Coulomb's Law. This problem is suitable for students in Grades 10-12, covering nuclear physics and algebraic principles.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation