# Atomic Decay and Heat capacity

9) 9. Calculate the decay constant of element Rn ,if during twenty four hours number of atoms decreases only to 18.2%?

1. $2.1*10^3 s^{-1}$

2. $2.1*10^{-5} s^{-1}$

3. $3.2*10^{-3} s^{-1}$

4. $2.1*10^6 s^{-1}$

5. $0.33*10^6 s^{-1}$

10)  There are two samples with the same dimensions: copper and iron. Which molar heat capacity is smaller

1.copper

2. Iron

3. Equally

9) The decay constant L is defined as

$N(t)= N0*exp(-L*t)$

where N0 is the initial number of atoms and N(t) is the remaining number of atoms after time t

$N0/N = exp(L*t)$

$1/0.182 =exp(L*24*3600)$

$L* 86400 =1.704$

$L =1.97*10^{-5} sec =2*10^{-5} sec$

Correct answer is 2) $2*10^{-5} sec$

10) The molar heat capacity of copper is $C(Cu) =24.47 J/(mol*K)$ and the molar heat capacity of iron is $C(Fe) =25.1 J/(mol*K)$.  Therefore  copper has a smaller molar heat capacity.