91Ó°ÊÓ

The kinetic energy of any particle relies upon the ‘mass’ and ‘velocity’ of the particle.

The formula for the kinetic energy (K.E.) of the particle having mass ‘m’ and velocity ‘v’ is given by,

$K.E.=\frac{1}{2}m{v}^2$

• The initial speed of the proton is $u=3000m/s$.
• The final speed of the proton is, $\mathrm{v}=5000\mathrm{m}/\mathrm{s}$.

The mass of the proton is given by,

$m=1.67×{10}^{-27}kg$

The formula for the initial kinetic energy of the proton is given by,

role="math" localid="1657080291356" $$\begin{gathered} {\mathrm{E}}_1=\frac{1}{2}{\mathrm{mu}}^2 \\ {\mathrm{E}}_1=\frac{1}{2}×1.67×{10}^{-27}\mathrm{kg}{\left(3000\mathrm{m}/\mathrm{s}\right)}^2×\frac{1\mathrm{J}}{1\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2} \\ {\mathrm{E}}_1=7.51×{10}^{-21}\mathrm{J} \end{gathered}$$

Hence, the initial kinetic energy of the proton is $7.51×{10}^{-21}\mathrm{J}$.

The formula for the final kinetic energy of the proton is given by,

$$\begin{gathered} {\mathrm{E}}_2=\frac{1}{2}m{v}^2 \\ {\mathrm{E}}_2=\frac{1}{2}×1.67×{10}^{-27}\mathrm{kg}{\left(5000\mathrm{m}/\mathrm{s}\right)}^2×\frac{1\mathrm{J}}{1\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2} \\ {\mathrm{E}}_2=20.87×{10}^{-21}\mathrm{J} \end{gathered}$$

Hence, the final kinetic energy of the proton is $20.87×{10}^{-21}\mathrm{J}$.

The formula for the change in the kinetic energy of the proton is given by,

$$\begin{gathered} ∆\mathrm{E}={\mathrm{E}}_2-{\mathrm{E}}_1 \\ ∆\mathrm{E}=20.87×{10}^{-21}\mathrm{J}-7.51×{10}^{-21}\mathrm{J} \\ ∆\mathrm{E}=13.36×{10}^{-21}\mathrm{J} \end{gathered}$$

Hence, the change in the kinetic energy of the proton is $13.36×{10}^{-21}\mathrm{J}$.