Pair Production Velocity Calculation

[ikihi]

Homework Statement

[/B]
A proton and anti-proton are created by a photon with wavelength λ= 6.607×10⁻⁷ nm. What is the magnitude of the velocity of the newly created proton and anti-proton pair? Note, the mass of a proton/anti-proton is mp= 1.673×10^-27 kg = 938.3M MeV/c².

Homework Equations

E_photon = h ⋅ c / λ
E₀ = m₀ ⋅ c²
KE = 0.5 ⋅ m ⋅ v²

The Attempt at a Solution

E_photon= 3.009 x 10^-10 J
E₀ = 1.506 x 10^-10 J

KE=E_photon - 2 ⋅ E₀ / (2)
KE= 3.009 x 10^-10 - 2 ⋅ 1.506 x 10^-10 J / (2)
KE_{of either particle}= -1.5 x 10^-13 J

 

[Bandersnatch]

E0 = 1.506 x 10-10 J

Google calculator shows 938.3 MeV=1.503E-10 Joules.

 

[patric44]

if you convert the energy of the photon to Mev and subtract from it (2*938.3 Mev) it will give a positive number
i guss the problem is the mass of the proton missing a lot of digits and the speed of light as well.
like Bandersnatch said if you use the full digits of the mass and speed of light it will give 1.503*10^-10

 

[ikihi]

Google calculator shows 938.3 MeV=1.503E-10 Joules.

I calculated E₀ using E₀ = m₀ ⋅ c². So is that the same as the given value?

 

[ikihi]

if you convert the energy of the photon to Mev and subtract from it (2*938.3 Mev) it will give a positive number
i guss the problem is the mass of the proton missing a lot of digits and the speed of light as well.
like Bandersnatch said if you use the full digits of the mass and speed of light it will give 1.503*10^-10

You are right. I converted both to MeV and it came out to KE = 0.029!

0.029 MeV ---> 4.646 x10^-15 J

I calculate that the speed is 2.36 x 10⁶ m/s.

However after using more sig fig digits the answer goes to 0 m/s. Maybe this is a relativistic problem that needs a different equation?

 

[haruspex]

after using more sig fig digits the answer goes to 0 m/s

That seems rather unlikely. If you cannot find a mistake please post all your working.