Chapter 32, Problem 16P

To determine

The total energy (E).

Answer to Problem 16P

Solution:

The total energy (E)is -739.1MeV.

Explanation of Solution

Given Info:

The mass of ${\Xi }^0$ is 1314.9MeV

The mass of ${\Lambda }^0$ is 1115.7 MeV.

The mass of P is 938.3 MeV.

The formula to calculate the energy is,

$\begin{array}{l}\text{E=}\left[{\text{m}}_{{\text{Ξ}}^{\text{0}}}\text{-}\left({\text{m}}_{{\text{Λ}}^{\text{0}}}{\text{+m}}_{\text{p}}\right)\right]{\text{c}}^{\text{2}}\\ {\text{E=m}}_{{\text{Ξ}}^{\text{0}}}{\text{c}}^{\text{2}}\text{-}\left({\text{m}}_{{\text{Λ}}^{\text{0}}}{\text{c}}^{\text{2}}{\text{+m}}_{\text{p}}{\text{c}}^{\text{2}}\right)\end{array}$

• E is the energy released in the process of decay.

• $m_{{\Xi }^0}$ is the mass of the ${\Xi }^0$. (1314.9Mev/c²)

• $m_{{\Lambda }^0}$ is the mass of the ${\Lambda }^0$. (1115.7MeV/c²).

• $m_p$ is the mass of proton. (938.3MeV/c²)

Substitute 1314.9 MeV/c² for ‘ $m_{{\Xi }^0}$’, 1115.7MeV/c² for ‘ $m_{{\Lambda }^0}$’ and 938.3MeV/c² for ‘ $m_p$’ to find E,

$\text{E=}\left(\text{1314}\text{.9}{\text{MeV/c}}^{\text{2}}\right){\text{×c}}^{\text{2}}\text{-}\left[\left(\text{1115}\text{.7}{\text{MeV/c}}^{\text{2}}\right){\text{×c}}^{\text{2}}\text{+}\left(\text{938}\text{.3}{\text{MeV/c}}^{\text{2}}\right){\text{×c}}^{\text{2}}\right]$

$\text{E=}\text{-}\text{739}\text{.1MeV}$ (I)