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An electron has a speed of 0.750 c .(a) Find the speed of a proton that has the same kinetic energy as the electron.

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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