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## Homework Statement

Thorium (with half-life T1/2 = 1.913 yr. and atomic mass 228.028715 u) undergoes alpha decay and produces radium (atomic mass 224.020186 u) as a daughter nucleus. (Assume the alpha particle has atomic mass 4.002603 u.)

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

Answer: 4.136E-5 hrs-1

The energy released from the decay of 10 g of thorium is used to heat 3.8 kg of water (assume all the energy released goes into the water).

**(c) What is the change in temperature of the water after 1 hr.?**

## Homework Equations

E=mc2

N0= Mtotal/Mparticle

N=N0e^-λt

Q=mcT

## The Attempt at a Solution

N0= Mtotal/Mparticle

N0=[(0.01kg)]/[(228.0287u)(1.66E-27kg)]

N0=2.64E22 atoms

N=N0e^-λt

N=(2.64E22 atoms)e^-(4.136E-5 hrs-1)(1hr)

N=2.642E22 atoms

mi=228.028715u

mf=224.020186u + 4.002603u

mf=228.022789u

m=mf-mi

m=228.022789u - 228.028715u

m=0.005926u

E=mc2

E=(0.005926u)[(931.5Mev/c2)/u]c2

E=5.52Mev

(5.52Mev)(1.602E-13J/Mev) = 8.843E-13 J

(8.843E-13J)(2.642E22 atoms)=2.336E10J

Q=mcT

2.336E10J=(3.8kg)(4186 J/kg-K)(T)

T=1468755.878 K = 1468482.878 C

Can someone help me catch my mistake? I'm not sure what I did wrong. Thank you.