Can Pair Production Occur if Positron and Electron Have the Same Rest Energy?

[Kiwithepike]

Homework Statement

If positron and electron have the same rest energy can pair production occur?

Homework Equations

E=hc/λ Plancks equation
E=mc^2

The Attempt at a Solution

so i found the E of the photons using Plancks equation
and found the photon E to be 6.83x10^-14 ( should I double this due to two photons required?)
so
for pair production the energy of the photons has to be at least the energy of mc^2
so i just added the positron and electrons masses and multiplied by c^2
and got 1.64x10^-13
did i do this correctly? so Ephoton < E of Positron and electron so no pair production can occur?
am i missing anything or do something wrong?

 

[vela]

You still seem to be leaving out information. Could you please post the entire text of the problem?

 

[Kiwithepike]

heres the first part
A. Use wiens law to determine the peak wavelength of blackbody photons where T = 10^9K
so λ= 2.9x10^-3 / 10^9
=> λ = 2.9x10^-12
then
B. use Planck Eq to determine the energy of the photons
E = hc/λ => E = (6.6x10^-25)(3x10^8)/ 2.9x10^-12 => E = 6.83x10^-14

C. The positron and electron where created by pair production (ie. Photon + photon --> Positron + Electron). If Both positron and electron have the same "rest energy" show whether or pair production can occur.
I tried using E=mc^2
I know that the energy of the photns must be atleast the energy of the posi and electron.
so mc^2 is the energy of the electron and positron.
used m as (9.109x10^-31)x2 since the positron and electron have the same mass.

 

[vela]

You need to include units on your numbers. You've calculated the individual energies correctiy. You just need to make sure the initial energy exceeds the minimum energy of electron-positron pair.

 

[Kiwithepike]

ok il make sure to add units,
just for clarification is the E i calculated in step B the initial ? and if it's not larger they can't be formed right?

thanks for all the help!