The nucleus of a 125Xe atom (an isotope of the element xenon with mass 125 u) is 6.0 fm in diameter. It has 54 protons and charge q = +54e.
Part A:
What is the electric force on a proton 1.4 fm from the surface of the nucleus?
Hint: Treat the spherical nucleus as a point charge.
Express your answer to two significant figures and include the appropriate units.
SOLUTION:
We know the formula for the force between two charged particles is F = K |q1| |q2| r-2
We simply have to determine which values to plug into this equation and we will get the answer that we're looking for.
Begin by taking the radius of the nucleus, which is half the diameter, or 3 fm
the added distance of the proton is 1.4 fm, so the total distance of the proton from the center of the nucleus is 3 + 1.4 = 4.4 fm = 4.4⋅10-15 m
so r = 4.4⋅10-15 m
Next we need to determine the two charges. We're given that the nucleus has a charge of q = +54e.
Knowing that e=1.6⋅10-19 C , qnucleus = 8.64⋅10-18 C
q1 = 8.64⋅10-18 C
lastly, we know that the charge of ONE proton is just e, so
q2 = 1.6⋅10-19 C
Now we have all of our values to plug in and can solve for the force(remember K is the electrostatic constant and equal to 9.0⋅109 Nm2/C2)
∴F = (9.0⋅109 Nm2/C2)(8.64⋅10-18 C)(1.6⋅10-19 C)(4.4⋅10-15 m)-2
→F = 642.645 NPart B:
What is the proton's acceleration?
Express your answer to two significant figures and include the appropriate units.
SOLUTION:
We know that F=ma, so if we divide the force by the given mass... a = 3.8×1029 m/s2
What did you convert the 125 u to for part B and how?
ReplyDelete1 u = 1.661 x 10^(-27) kg
DeletePart B's answer seems completely unreasonable as it exceeds the speed of light (3.00x10^8)
ReplyDeleteThis comment has been removed by the author.
DeleteSpeed and acceleration aren't the same
ReplyDeletePart B asks for the acceleration of the Proton. So look up the mass of a Proton. The mass of the Xe isotope it gives you is irrelevant to this problem.
ReplyDelete