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Sagot :
By relativistic energy, the proton speed is 0.024c.
We need to know about relativistic energy to solve this problem. The rest energy of the object can be determined by
Eo = m₀ . c²
where Eo is rest energy, m₀ is rest mass and c is speed of light (3 x 10⁸ m/s).
The total energy of object can be described as
E = Eo / √(1 - v²/c²)
where E is total energy, v is the object speed.
The kinetic energy is
KE = E - Eo
From the question above, we know that :
mp = 1.6 x 10¯²⁷ kg
me = 9.1 x 10¯³¹ kg
c = 3 x 10⁸ m/s
ve = 0.75c
Find the rest energy of electron
Eo = me . c²
Eo = 9.1 x 10¯³¹ . (3 x 10⁸)²
Eo = 8.19 x 10¯¹⁴ joule
Eo = 8.19 x 10¯¹⁴ / (1.6 x 10¯¹⁹) eV
Eo = 511875 eV
Determine the total energy of electron
E = Eo / √(1 - ve²/c²)
E = 511875 / √(1 - (0.75c)²/c²)
E = 511875 / 0.66
E = 773882.26 eV
Calculate the kinetic energy of electron
KE = E - Eo
KE = 773882.26 - 511875
KE = 262007.26 eV
Find the rest energy of proton
Eo = mp . c²
Eo = 1.6 x 10¯²⁷ . (3 x 10⁸)²
Eo = 1.44 x 10¯¹⁰ joule
Eo = 1.44 x 10¯¹⁰ / (1.6 x 10¯¹⁹) eV
Eo = 900000000 eV
Determine the total energy of proton
E = KE + Eo
E = 262007.26 + 900000000
E = 900262007.3 eV
Find the speed of proton
900262007.3 = 900000000 / √(1 - v²/c²)
√(1 - v²/c²) = 0.9997
1 - v²/c² = 0.9994
v²/c² = 1 - 0.9994
v²/c² = 5.82 x 10¯⁴
v² = 5.82 x 10¯⁴ c²
v = 0.024c
Find more on relativistic energy at: brainly.com/question/23920189
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