An alpha particle (charge = +2.0e) is sent at high speed toward a gold nucleus (charge = +79e). What is the electric force acting on the alpha particle when the alpha particle is 3.3 ✕ 10-14 m from the gold nucleus?
k Q1 Q2/ d^2
Me no kow
To calculate the electric force between the alpha particle and the gold nucleus, we can use Coulomb's law:
The formula for Coulomb's law is:
F = k * ((q1 * q2) / r^2)
Where:
F is the electric force
k is the electrostatic constant = 8.99 x 10^9 N m^2/C^2
q1 and q2 are the charges of the particles
r is the distance between the particles
Given:
q1 = charge of the alpha particle = +2.0e = +2.0 * 1.6 x 10^-19 C
q2 = charge of the gold nucleus = +79e = +79 * 1.6 x 10^-19 C
r = distance between the particles = 3.3 x 10^-14 m
Substituting these values into the formula:
F = (8.99 x 10^9 N m^2/C^2) * ((2.0 * 1.6 x 10^-19 C) * (79 * 1.6 x 10^-19 C) / (3.3 x 10^-14 m)^2)
First, let's calculate the product of the charges:
(2.0 * 1.6 x 10^-19 C) * (79 * 1.6 x 10^-19 C) = 6.4 x 10^-19 C^2
Now, let's calculate the square of the distance:
(3.3 x 10^-14 m)^2 = 1.089 x 10^-27 m^2
Finally, substitute these values into the formula to find the electric force:
F = (8.99 x 10^9 N m^2/C^2) * (6.4 x 10^-19 C^2 / 1.089 x 10^-27 m^2)
Calculate the product of the charges:
F = (8.99 x 10^9 N m^2/C^2) * (5.886 x 10^-8 N)
F = 5.288 x 10^-8 N
Therefore, the electric force acting on the alpha particle when it is 3.3 x 10^-14 m from the gold nucleus is 5.288 x 10^-8 N.
To calculate the electric force acting on the alpha particle, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = (k * |q1 * q2|) / r^2
Where:
F is the electric force between the two charges
k is the electrostatic constant, approximately equal to 9.0 x 10^9 Nm^2/C^2
q1 and q2 are the charges of the alpha particle and the gold nucleus, respectively
|q1 * q2| is the absolute value of the product of their charges
r is the distance between the charges
In this case, the charge of the alpha particle is +2.0e (where e is the elementary charge, 1.6 x 10^-19 C), the charge of the gold nucleus is +79e, and the distance between them is 3.3 x 10^-14m.
Let's substitute these values into the formula:
F = (k * |q1 * q2|) / r^2
F = (9.0 x 10^9 Nm^2/C^2 * |+2.0e * +79e|) / (3.3 x 10^-14m)^2
Now, let's calculate the electric force:
F = (9.0 x 10^9 Nm^2/C^2 * 2.0e * 79e) / (3.3 x 10^-14m)^2
First, let's simplify the charges' product:
q1 * q2 = (2.0e * 79e) = 158e^2
Now substitute the simplified expression back into the formula:
F = (9.0 x 10^9 Nm^2/C^2 * 158e^2) / (3.3 x 10^-14m)^2
Calculate the exponent of e:
F = (9.0 x 10^9 Nm^2/C^2 * 158 * (1.6 x 10^-19 C)^2) / (3.3 x 10^-14m)^2
Now calculate the final expression to find the electric force acting on the alpha particle.