A single photon in empty space is converted into an positron and an electron, each with rest mass 511Mev.
(a) show this transformation is not possible (dynamaically).
(b)How could this transformation be made posible.
(c)what is the minimum photon energy required to enable the process in part b.
please show working
I have nothing more to add to my previous answer.
ttp://www.jiskha.com/display.cgi?id=1307558664
There should have been an "h" at the beginning of the link I posted.
For a discussion of why a third body is required for pair creation, see
http://books.google.com/books?id=GgFjLiZDOk8C&pg=PA118&lpg=PA118&dq=electron+positron+creation+third+body&source=bl&ots=w0H9QEXfMC&sig=_0Cl-HfHIyIdgCE5xlKSMCqckog&hl=en&ei=oUf1TcTpD-XRiAKzl5mGBw&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCIQ6AEwAg#v=onepage&q=electron%20positron%20creation%20third%20body&f=false
(a) To determine whether this transformation is dynamically possible, we need to consider energy and momentum conservation.
Let's assume that the initial photon has energy E and moves along the x-direction. Since the photon is at rest before the transformation, its momentum is zero.
After the transformation, we have one positron and one electron. The momentum of each of these particles can be calculated using the equation:
p = sqrt(E^2 - (rest mass)^2)
For the electron, its momentum magnitude is given by:
p_electron = sqrt(E^2 - (511 Mev)^2)
For the positron, its momentum magnitude is also:
p_positron = sqrt(E^2 - (511 Mev)^2)
According to the conservation of momentum, the total momentum before the transformation must be equal to the total momentum after the transformation:
0 = p_electron + p_positron
However, since both p_electron and p_positron have the same magnitude, their sum can never be zero. Therefore, the transformation of a single photon into an electron-positron pair in empty space is not dynamically possible.
(b) To make this transformation possible, we need to introduce another particle that carries away the excess momentum. One way to achieve this is through the presence of a nearby nucleus or another particle, which can absorb the momentum difference. In this case, the nucleus (or another particle) would recoil in the opposite direction, conserving overall momentum.
(c) The minimum photon energy required to enable the process in part (b) can be found by considering the rest mass energy of the electron-positron pair:
(rest mass energy) = 2 × (rest mass energy of electron) = 2 × (511 Mev) = 1022 Mev
In addition to the energy required for the creation of the electron-positron pair, we need to account for the energy used to overcome the binding energy of the nucleus (or other particle) involved in the process.
Therefore, the minimum photon energy required is the sum of the electron-positron pair's rest mass energy and the binding energy of the nucleus (or other particle). The specific value of the binding energy depends on the system under consideration.