To practice Problem-Solving Strategy 21.1 Conservation of energy in charge inter

Question

To practice Problem-Solving Strategy 21.1 Conservation of energy in charge interactions.

An alpha particle (), which is the same as a helium-4 nucleus, is momentarily at rest in a region of space occupied by an electric field. The particle then begins to move. Find the speed of the alpha particle after it has moved through a potential difference of 3.45×103 V .

The charge and the mass of an alpha particle are q = 3.20×1019 C and m = 6.68×1027 kg , respectively.

If you had carried out the algebra using variables before plugging numbers into your expressions, you would have found that

(vf)=2qVm,

where V is measured in volts. To verify that this expression for (vf) has the correct units of velocity, you need to perform some unit analysis. Begin by finding the equivalent of a volt in terms of basic SI units. What is a volt in terms of meters (m), seconds (s), kilograms (kg), and coulombs (C)?

answer includes C

Explanation / Answer

vf=sqrt( 2qV/ m )

V = Joule /coulomb = J/C

J = Newtom * m = N*m

N = kg*m/s^2

so,

V =( kg*m/s^2) *m /C

= kg m^2/(s^2*C)

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