Question

What is the mass (in kg) of the$Z^{°}$? What is the ratio of the mass of the to the mass of the$Z^{°}$ proton?

Short answer

Mass of $Z^{°}$is $1.635\times {10}^{-25}kg$ The ratio of the mass of the$Z^{°}$ to the mass of the proton is$97.1992$

Step-by-step solution

Mass of Z°

Mass of $Z^{°}$ particle is $m_z=91.2GeV/c^2$

calculate mass of Z° in kg hence find ratio

Mass of $Z^{°}$particle is $m_z=91.2GeV/c^2$

Mass of$Z^{°}$in atomic mass units is,

$$\begin{gathered} m_z=91.2\times {10}^{3}MeV/c^2(c^2/(931.5MeV/u\left)\right) \\ {m}_z=97.906602u \end{gathered}$$

Now, it is known that role="math" localid="1663947806501" $1u=1.67\times {10}^{-27}kg$

This results in,

$$\begin{gathered} m_z=97.906602\times 1.67\times {10}^{-27} \\ {m}_z=1.635\times {10}^{-25}kg \end{gathered}$$

The mass of proton is $m_p=1.007276u.$

The ratio of mass of $Z^{°}$to mass of proton is,

$$\begin{gathered} m_z/m_p=97.906602u/1.007276u \\ {m}_z/m_p=97.1992 \end{gathered}$$

Therefore, Mass of $Z^{°}$is $1.635\times {10}^{-25}kg$. The ratio of the mass of the to the$Z^{°}$ mass of the proton is