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Chapter 22: Q. 37 (page 625)

The nucleus of a125Xeatom (an isotope of the element xenon with mass 125u) is 6.0fmin diameter. It has 54protons and charge q=+54e.

a. What is the electric force on a proton 2.0fmfrom the surface of the nucleus?

b. What is the proton鈥檚 acceleration?

Hint: Treat the spherical nucleus as a point charge

Short Answer

Expert verified

(a) The electric force of proton F=497.6N.

(b) The acceleration of the protona=2.99脳1029ms2.

Step by step solution

01

Find electric force (part a)

Because a proton is 2.0fmfrom the SURFACE of the Xenon atom, you must add the 2.0fmto the radius of the Xeatom, resulting in a distance of 5.0fmbetween neutron and the centre of the Xeatom.

2fm+3fm=5fm=5脳10鈭�15m

We must now determine the number of currently operates by the Xeatom. Because there are 54protons in the problem, we must increase it by the charge of a proton, which is 1脳10鈭�19C.

541脳10鈭�19C=8.64脳10鈭�18C

Substitute F=kq1q2r2in equation andk=9脳109Nm2C2

F=kq1q2r2

F=k8.64脳10鈭�18C1.6脳鈭�19C5脳10鈭�15m2

F=497.6N

02

Find the acceleration of proton (part b)

To find the proton's force, use Newton's F=maequation. In the equation, use the charge of a proton.

F=m脳a

a=Fm

a=497.6N1.661脳10鈭�27Kg

a=2.99脳1029ms2

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