Answer
557.9 W or 557.9 J/s
Work Step by Step
To find the rate of alpha decay, use the power output formula
$P = RQ$
where
$R=\lambda N = \frac{N ln 2}{T_{1/2}} $
Find the number of particles involved (N)
$N = \frac{M_{total}}{m_{Pu}}$
$N = \frac{1.00 kg}{(238 u)(1.661\times 10^{-27}kg/u)} = 2.53\times10^{24} $
Rearrange the equation,
$P=\frac{NQ ln 2}{T_{1/2}} $
and the half life $87.7 years = 2.766 \times 10^9 s$
$Q = 5.50 MeV$
$ P = \frac{(2.53\times10^{24}) (5.50 \times 10^6 eV) (1.6 \times 10^{-19} J/eV)(ln2)}{2.766 \times 10^9 s}$
$P = 557.9 W$
