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Chapter 25: Q. 14 (page 709)

What potential difference is needed to accelerate a He+ion (charge +e,mass4u) from rest to a speed of2.0脳106m/s?

Short Answer

Expert verified

鈭�V=8.35脳104V

Step by step solution

01

Given information and theory used  

Given :

Element : He+ion (charge +e,mass4u)

To accelerate to a speed of : 2.0脳106m/s

Theory used :

From the equation of conservation of energy, we have :

q鈭�V=m2(vf2-vi2)

02

Calculating potential difference needed  

Because all of the energy from the electric field is changed to kinetic energy, we get :

q鈭�V=mvf22

Taking into account the fact that there is no beginning velocity, we will have that. We may now write the solution as

鈭�V=mvf22q.

The potential difference can be calculated as 鈭�V=mv222qbecause the initial velocity is zero.

We get 鈭�Vby substituting the supplied numerical values :

鈭�V=4脳1.67脳10-27(2脳106)22脳1.6脳10-19鈭�V=8.35脳104V

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Most popular questions from this chapter

Two 2.00cm脳2.00cm plates that form a parallel-plate capacitor are charged to 0.708 nC. What are the electric field strength inside and the potential difference across the capacitor if the spacing between the plates is (a) 1.00 mm and (b) 2.00 mm?

Show that 1V/m=1N/C.

Two spherical drops of mercury each have a charge of 0.10nC and a potential of 300Vat the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?

Two positive point charges q are located on the y-axis aty=卤12s.

a.Find an expression for the potential along the x-axis.

b.Draw a graph of V versus x for -鈭�<x<鈭�. For comparison, use a dotted line to show the potential of a point charge 2qlocated at the origin.

FIGUREQ25.2shows the potential energy of a proton q=+eand a lead nucleusq=+82e. The horizontal scale is in units of femtometers, where 1fm=10-15m.

aA proton is fired toward a lead nucleus from very far away. How much initial kinetic energy does the proton need to reach a turning point10fm from the nucleus? Explain.
bHow much kinetic energy does the proton of part a have when it is20fmfrom the nucleus and moving toward it, before the collision?
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