Question

Calculate the speed of a moving proton whose kinetic energy is 5 MeV. The mass of the proton is 1.6 × 10⁻²⁷ kg and 1 MeV = 1.6 × 10⁻¹³ J.

Answer 1

Given Data:

Kinetic Energy (KE) = 5 MeV

Mass of the proton (m) = 1.6 × 10⁻²⁷ kg

Conversion factor: 1 MeV = 1.6 × 10⁻¹³

Convert Kinetic Energy into Joules (J):

KE = 5 × 1.6 × 10⁻¹³ J

= 8.0 × 10⁻¹³ J

Apply the Kinetic Energy formula:

KE = `1/2 mv^2`

`v^2 = (2 xx KE)/m`

`v^2 = (2 xx 8.0 xx 10^-13)/(1.6 xx 10^-27)`

`v^2 = (16.0 xx 10^-13)/(1.6 xx 10^-27)`

v² = 10 × 10¹⁴

v = `sqrt(10 xx 10^14)`

v = `sqrt10 xx 10^7`

v ≈ 3.16 × 10⁷ m/s

The speed of the moving proton is 3.16 × 10⁷ m/s.