An alpha particle ( ), which is the same as a helium-4 nucleus, is momentarily a

Question

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.

f 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)?

Express your answer using the symbols for the units meters, seconds, kilograms, and coulombs.

Explanation / Answer

From the definition of the Volt unit ( 1V pd = 1J of energy transferred to/from each Coulomb of charge passing between two points) ..

EPE loss = pd (J/C) x q (C) = -3.45^-3J/C x +3.20^-19C .. .. U = - 1.10^-21 J

By conservation of energy .. loss of electrical PE(U) = KE gained(½mv²)
1.10^-21J = ½ x 6.68^-27kg x v²

v = (2 x 1.10^-21 / 6.68^-27) .. .. v = 574.0 m/s

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