Answer:
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) = ([tex]\frac{1}{2}[/tex])(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) = ([tex]\frac{1}{2}[/tex])(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.
