Question

What should be minimum wavelength (in $A^o$) of a photon if it has to show pair production?

Answer 1

For a photon to show pair production :

$hv{=}_{-1}^0\text{e}{+}_{+1}^0\text{e}$, since two particles (i.e., position and electron) are formed, the minimum energy associated with photon should be at least equal to $E=2\times m_e\times c^2$(where $c$ is velocity of light)

$E=2\times 9.11\times {10}^{-31}\times (3.0\times {10}^8{)}^2=1.64\times {10}^{-13}J$

Also, $E=\frac{hc}{\lambda }$

$\therefore \lambda =\frac{6.626\times {10}^{-34}\times 3.0\times {10}^8}{1.64\times {10}^{-13}J}=1.2\times {10}^{-12}m=121A^o$

Since, $E\propto \frac{1}{\lambda }$

Thus, the minimum wavelength of photon should be $121A^o$.

This wavelength belongs to $X-$rays.