Question

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 (1 fm = 1 femtometer = 1×10−15m.) Hint: Treat the spherical nucleus as a point charge. Part A Part complete What is the electric force on a proton 1.0 fm from the surface of the nucleus? Express your answer in newtons. Fnucleusonproton F n u c l e u s o n p r o t o n = 780 N SubmitPrevious Answers Answer Requested Part B What is the proton's acceleration? Express your answer in meters per second squared.

Answer 1

A:
`777.6\ N.`

B:
`\rm 4.656* 10^(29)\ m/s^2.`

Step-by-step explanation:

Given:

• Charge on the 125 Xe nucleus,
  `\rm q = +54e.`

• Diameter of the 125 Xe nucleus,
  `\rm d=6.0\ fm = 6.0* 10^(-15)\ m.`

• Distance of the proton from the surface of the nucleus,
  `\rm a=1.0\ fm = 1.0* 10^(-15)\ m.`

Part A:

Coulomb's law states that the electric field due to a charged sphere of charge Q at a point r distance away from its center is given by

`\rm E=(kQ)/(r^2).`

where, k = Coulomb's constant whose value =
`9* 10^9\ \rm Nm^2/C^2.`

Therefore, the electric field due to the nucleus at the proton is given by

`\rm E=(kq)/(r^2)=((9* 10^9)* (+54 e))/(r^2)`

• 
  `\rm e` = elementary charge, having value = \rm 1.6\times 10^{-19}\ C.

• 
  `\rm r` = distance of the proton from the center of the nucleus =
  `\rm a+\text{Radius of the nucleus}= a + \frac d2 = 1.0+\frac{6.0}2=4.0\ fm = 4.0* 10^(-15)\ m.`

Therefore,

`\rm E=((9* 10^9)* (+54 * 1.6* 10^(-19)))/((4.0* 10^(-15))^2)=4.86* 10^(21)\ N/C.`

The electric force on a charge q due to an electric field is given as

`\rm F=qE`

For the proton,
`\rm q = e =1.6* 10^(-19)\ C.`

Thus, the electric force on the proton is given by

`\rm F = 1.6* 10^(-19)* 4.86* 10^(21)=777.6\ N.`

Part B:

According to Newton's second law,

`\rm F=ma`

where, a is the acceleration.

The mass of the proton is
`\rm m_p=1.67* 10^(-27)\ kg.`

Therefore, the proton's acceleration is given by

`\rm a = (F)/(m_p)=(777.6)/(1.67* 10^(-27))=4.656* 10^(29)\ m/s^2.`