# Why do I keep getting the lifetime of the W boson as being $10^{-15}$ rather than $10^{-25}$?

I need to calculate the lifetime of the W boson given its decay width. From what I know the lifetime of a particle is calculated by dividing $$\hbar$$ with the decay width $$\Gamma$$. From my textbook $$\Gamma=2.141$$ GeV, and $$\hbar=6.852 \times10^{-15}$$Gev$$\cdot$$s, doing the lifetime calculation with these values gives me:

$$\tau=\hbar/\Gamma\approx3.2\times10^{-15}s$$

I know the correct solution is $$3.2\times10^{-25}s$$, but I can't for the life of me figure out how to get that number. What am I missing here?

• Which unit has $\hbar=6.852 \times10^{-15}$? eVs, or GeVs, or something else? Commented Jun 13, 2019 at 17:23
• @ThomasFritsch I apologize, the units are Gev$\cdot$s. I have edited my post. Commented Jun 13, 2019 at 17:26
• Look at Wikipedia:Planck constant. They have $\hbar = 6.582 \cdot 10^{-16}$ eVs. (i.e. without G) Commented Jun 13, 2019 at 17:31
• You seem to have done an incorrect conversion from $eV$ to $GeV$ as $\hbar = 6.582\times 10^{-16}eV \cdot s$, and $1 \; eV = 10^{-9}\; GeV$ Commented Jun 13, 2019 at 17:31
• The Google calculator says hbar/(2.141 GeV) is $3.07432018\times 10^{-25}$ seconds. Commented Jun 13, 2019 at 17:34