Two alpha particles (helium nuclei) are held in place 1.0 nm apart (use 120 on for the diameter of a helium atom). Compare the electric and gravitational forces acting between the two nuclei.
To compare the electric and gravitational forces acting between two alpha particles, we need to use the formulas for these forces and calculate their magnitudes.
1. Electric Force: The electric force between two charged particles is given by Coulomb's law. The formula for electric force is:
F_electric = k * (q1 * q2) / r^2
where F_electric is the electric force, k is the electrostatic constant (9.0 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between the particles.
2. Gravitational Force: The gravitational force between two particles is given by Newton's law of gravitation. The formula for gravitational force is:
F_gravity = G * (m1 * m2) / r^2
where F_gravity is the gravitational force, G is the universal gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the particles, and r is the distance between the particles.
Now, let's calculate the magnitudes of the electric and gravitational forces acting between the two alpha particles.
Given:
Distance between alpha particles (r) = 1.0 nm = 1.0 x 10^-9 m (converted to meters)
1. Electric Force:
Charge of an alpha particle (helium nucleus) = 2e (where e is the elementary charge = 1.6 x 10^-19 C)
F_electric = (9.0 x 10^9 Nm^2/C^2) * [(2e) * (2e)] / (1.0 x 10^-9 m)^2
2. Gravitational Force:
Mass of an alpha particle (m) = 4.0 atomic mass units (approximately)
F_gravity = (6.67 x 10^-11 Nm^2/kg^2) * [(4.0 amu) * (4.0 amu)] / (1.0 x 10^-9 m)^2
Now, plug in the values and calculate the magnitudes of the forces.
Note: since "comparing" the forces means finding the ratio between them, we can also simplify the calculations further by dividing the two forces.
Final Answer:
Calculate F_electric and F_gravity using the formulas above and find their ratio.
The resulting ratio will provide a comparison between the magnitudes of the electric and gravitational forces acting between the two alpha particles.