91Ó°ÊÓ

The pion is initially at rest

The decay can be given as

${\mathrm{π}}^0→\mathrm{γ}+\mathrm{γ}$

Conservation of momentum

According to the law of conservation of momentum, if the system is closed then the total momentum of the system will remain constant.

According to the Conservation of momentum, the gamma-ray particles move in opposite directions with momenta of the same magnitude.

The Energy can be given as

E=pc

Where p is momentum and c is the velocity of light

Since gamma rays have the same momentum, therefore, they must have the same energy.

We know that the Energy of pion is

$E_{\mathrm{π}}=m_{\mathrm{π}}{c}^2= 135.0 \mathrm{MeV}$

Therefore, the energy of each $\mathrm{λ}$ produced

We know that wavelength can be given as

$\mathrm{λ}=\frac{hc}{E}$

Where E is energy, c is the velocity of light and h is plank constant

And the standard value of hc=1240 eV .nm

Now substituting all the values in the formula

$\begin{array}{c}\mathrm{λ}=\frac{hc}{E_{\mathrm{γ}}}\\ =\frac{1240  \mathrm{eV}. \mathrm{nm}}{67.5×{10}^{-6} \mathrm{eV}}\\ =1.84×{10}^{-5} \mathrm{nm}\\ =1.84  \mathrm{fm}\end{array}$

Therefore, the wavelength of each$\mathrm{λ}$produced is 1.84 fm

Wavelength,

$\mathrm{λ}=\frac{hc}{E}$

Where p is momentum and h is plank constant

Since both have the same magnitude of momentum, therefore their wavelength must be the same.