Determine the speed of an alpha particle with a kinetic energy of 22.3 eV.

Speed of alpha particle = 4.020 x 10¹⁷ m/s.

Explanation:

Given,

kinetic energy of alpha particle (K.E) =  22.3 eV

speed of alpha particle = ?

Kinetic energy of the alpha particle can be calculated by using the formula,

Kinetic energy (K.E) = ()(mv)²

where m =  mass of alpha particle

v = speed of alpha particle

As mass of alpha particle = 6.64424 x 10⁻²⁷ kg

Before proceeding further we have to convert Kinetic energy into Joules.

Since, 1 eV = 1.60 x 10⁻¹⁹ Joules.

Kinetic energy (K.E)  = 22.3 eV = 22.3 x 1.60 x 10⁻¹⁹ Joules

Kinetic energy (K.E) in Joules = 35.68 x 10⁻¹⁹ Joules.

substituting all values in the formula and solving we get,

Kinetic energy (K.E) = ()(mv)²

35.68 x 10⁻¹⁹ Joules = (0.5)(6.64424 x 10⁻²⁷ kg x v)²

=> (6.64424 x 10⁻²⁷ x v)² = (35.68 x 10⁻¹⁹/0.5)

=> (6.64424 x 10⁻²⁷ x v)² = 71.36 x 10⁻¹⁹

=> (6.64424 x 10⁻²⁷ x v) = 2.671 x 10⁻⁹

=> v = 4.020 x 10¹⁷ m/s.

Therefore speed of alpha particle = 4.020 x 10¹⁷ m/s.

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