Pair Production

Calculate the wavelength of the least energetic photon capable of producing an electron-positron pair in meters.


The answer is 1.21E-12.

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3 solutions

Hamza A
Jan 17, 2016

Frank Aiello
Jan 27, 2018

E = h v E = hv

v v = c λ \frac{c}{\lambda}

Minimum energy \textit{Minimum energy}

= 2 m e v 2 2m_{e}v^2

= 2 ( 9.1 1 0 31 k g ) 2(9.1 * 10^{-31} kg) ( 3 1 0 8 m / s ) 2 (3 * 10^8 m/s)^2

= 1.638 1 0 13 J 1.638 * 10^{-13} J

= 1.022 1.022 M e V MeV

Minimum frequency \textit{Minimum frequency}

= 2 m e v 2 h \frac{2m_{e}v^2}{h}

= 2 ( 9.1 1 0 31 k g ) ( 3 1 0 8 m / s ) 2 6.626 1 0 34 J s \frac{2(9.1 * 10^{-31} kg)(3 * 10^8 m/s)^2}{6.626 * 10^{-34} J s}

= 2.472 1 0 20 2.472 * 10^{20} H z Hz

Minimum wavelength \textit{Minimum wavelength}

= c f r e q u e n c y \frac{c}{frequency}

= 3 1 0 8 m / s 2.472 1 0 20 H z \frac{3 * 10^8 m/s}{2.472 * 10^{20} Hz}

= 1.2 1 0 12 1.2 * 10^{-12} m m

Ali Hyder
Jan 18, 2016

This is the threshold wavelength of an incoming photon in pair production. Simply use the photoelectric effect formula of hv and set it equal to two electron (neglecting nuclear recoil)...and solve in terms of wavelength! :)

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