A proton has the total energy 950 MeV. What's its speed?

1 Answer

Relevance
  • Unern
    Lv 4
    9 years ago
    Favorite Answer

    We are going to use this formula to find the velocity:

    E = m_0 c²/√(1–v²/c²)

    Where E is the total energy, m_0 is the rest mass, c is the speed of light and v is the velocity.

    The rest mass of a proton is 1.67 × 10^(-27) kg.

    The speed of light is 3.00 × 10^8 m/s.

    First, write the energy in joules:

    1 MeV = 1.602 × 10^(-13) J

    So:

    950 MeV = 950 × 1.602 × 10^(-13) J

    . . . . . . . = 1.522 × 10^(-10) J

    The next step is to write the formula E = m_0 c²/√(1–v²/c²) on this form: v/c = ...

    E = m_0 c²/√(1–v²/c²)

    √(1–v²/c²) = m_0 c²/E

    1–v²/c² = (m_0 c² / E)²

    v²/c² = 1 – (m_0 c² / E)²

    v/c = √(1 – (m_0 c² / E)²)

    Now, put in the correct values for m_0, c and E.

    v/c = √(1 – (1.67×10^(-27) × (3.00×10^8)² / (1.522×10^(-10)))²)

    v/c = 0.16

    So the velocity is v = 0.16 c.

    • Login to reply the answers
Still have questions? Get your answers by asking now.