Thorium $($with half$-$life $T_{\frac{1}{2}}=1\mathrm{.}913$ yr$.$ and atomic mass $228\mathrm{.}028715$ u undergoes alpha decay and produces radium $($atomic mass $224\mathrm{.}020186$ u $)$ as a daughter nucleus. $($Assume the alpha particle has atomic mass $4\mathrm{.}002603$ u$.)$

What is the decay constant of thorium? $($Note that the answer must be in units of hrs ${?}^{-1}.)$

$=hr{s}^{-1}$

What percent of thorium is left after $200$ days?

Percentage $\%$

$3.$ The energy released from the decay of $10$ g of thorium is used to heat $3\mathrm{.}8$ kg of water $($assume all the energy released goes into the water$).$ What is the change in temperature of the water after $1$ hour?

$T=$ K