# Question #e70bd

##### 1 Answer

This is what I get for parts (i) to (iii)

#### Explanation:

Nuclear decay formula using half-life is

#N_t=N_0 xx2^((-t)/T_(1//2))# ......(1)

where#N_t# is sample of radioactive material remaining after time#t# ,#N_0# is initial amount of sample and#T_(1//2)# is half life of the sample.

The formula can also be written as

#N_t=N_0 xxe^((-0.693t)/T_(1//2))# ......(2)

(i) Using equation (1)

#10^5=N_0 xx2^((-32)/2)#

#=>N_0 =10^5/2^((-32)/2)#

#=>N_0 =10^5xx2^16#

#=>N_0 =6.5536xx10^9#

(ii) Time

We know that half-life for a given radioactive sample is the time for half the radioactive nuclei in that sample undergo radioactive decay.

#:.t=T_(1//2)=2s#

(iii) Inserting result of part (i) and given values in equation (1) we get

#N_t=(6.5536xx10^9)xx2^((-4096)/2)#

#N_t=390.625#

#N_t=390# , rounded to previous lower integer. (as fraction of nucleus can not decay.