Answer:
[tex]v=1.54\times 10^{7}}\ \textup{m/s}[/tex]
Explanation:
Given:
The accelerated energy, U = 1.25 MeV = 1.25 × 10⁶ eV
we know,
1 eV = 1.6 × 10⁻¹⁹ J
thus,
1.25 eV = (1.6 × 10⁻¹⁹) × (1.25) J = 2 × 10⁻¹³ J
Now, Applying the law of conservation of energy, the energy due to acceleration will be equal to the kinetic energy
mathematically,
K.E = U
[tex]\frac{1}{2}mv^2=2\times 10^{-13} \ \textup{J}[/tex]
where,
m = mass of the particle = 1.67 × 10⁻²⁷ kg
v = velocity of the particle
on substituting the values we get
[tex]\frac{1}{2}\times 1.67\times 10^{-27}\times v^2=2\times 10^{-13} \ \textup{J}[/tex]
or
[tex]v^2=\frac{2\times 10^{-13}}{1.67\times 10^{-27}}[/tex]
or
[tex]v=\sqrt{2.39\times 10^{14}}[/tex]
or
[tex]v=1.54\times 10^{7}}\ \textup{m/s}[/tex]
