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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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