Question

One mediator of the weak interaction is the w- boson, with mass 80.4 GeV/c. Use this information to calculate the range of the weak interaction

Answer 1

The the range of the weak interaction is
`1.222*10^(-18)\ m`.

Step-by-step explanation:

Given that,

Mass = 80.4 GeV/c

We need to calculate the mass in kg.

We know that,

`1 GeV/c =1.79*10^(-27)\ kg`

`80.4 GeV/c = 1.79*10^(-27)*80.4\ kg`

`80.4 GeV/c =1.4391*10^(-25)`

We need to calculate the range of the weak interaction

Using formula of the range

`R=(\hbar)/(2mc)`

Here,
`\hbar = (h)/(2\pi)`

`R=(h)/(4\pi mc)`

Where, m = mass c = speed of light

Put the value into the formula

`R=(6.63*10^(-34))/(4\pi *1.4391*10^(-25)*3*10^(8))`

`R=1.222*10^(-18)\ m`

Hence, The the range of the weak interaction is
`1.222*10^(-18)\ m`.