Question

A container holds a pure sample of a radioactive substance with a half-life of 2 hours.Part AWhich of the following statements are true?Check all that apply.View Available Hint(s)Check all that apply.After 1 hour, less than 50% of the original atoms in the container will have decayed.After 1 hour, more than 50% of the original atoms in the container will have decayed.After 2 hours, 50% of the original atoms in the container will have decayed.After 4 hours, 25% of the original atoms will have decayed.After 4 hours, the total number of atoms in the container will be reduced by 75%.Part B Complete previous part(s)

Answer 1

Answer:

Step-by-step explanation: Half life period means half of the initial amount will be remaining after decay which is the same as half of the initial amount is decayed.  

Nt= N0 *1/2 ^ (t/th)  

After one hour Nt = N0 *√ 0.5 ^ (1/2) =0.7 N0 remaining or 0.3 has decayed  

Hence it is TRUE that  

After 1, less than 50 %of the original atoms in the container will have decayed  

But the statement  

After 1 hours, more than 50% of the original atoms in the container will have decayed is false.  

======================================...  

After 2 hours  

Nt= *0.5 ^ (2/2) N0= 0.5 N0 is remaining and 0.5 of N0 has decayed.  

Hence it is TRUE that  

After 2 hours, 50% of the original atoms in the container will have decayed.  

======================================...  

After 4 hours  

Nt= 0.5 ^ (4/2) N0= 0.5^2 N0 = 0.25 N0 is remaining or 0.75N0 has decayed.  

Hence it is false that  

After 4 hours, 25 %of the original atoms will have decayed and  

After 4 hours, 25 %of the original atoms will have decayed  

======================================...

Answer 2

Half life period means half of the initial amount will be remaining after decay which is the same as half of the initial amount is decayed.  

 $N_t = N_0 ( \frac{1}{2}) ^{\frac{t}{th} }$

• After one hour

$N_t = N_0( \frac{1}{2} )^{\frac{1}{2} }$ =0.7 $N_0$ remaining or 0.3 has decayed  

It states that After 1, more than 50%  of the original atoms in the container will have decayed .          

The given statement states that ,

After 1 hours, more than 50% of the original atoms in the container will have decayed is false.  

• After 2 hours  

$N_t = N_0(2)^{\frac{1}{2} }$ = 0.5 $N_0$ is remaining and 0.5 of N0 has decayed.  

 Hence it is true that  ; After 2 hours, 50% of the original atoms in the container will have decayed.  

 

After 4 hours ,

$N_t = N_0( \frac{4}{2} )^{\frac{1}{2} }$ = 0.5^2 N0 = 0.25 N0 is remaining or 0.75N0 has decayed.  

Hence it is false After 4 hours, 25 % of the original atoms will have decayed and   After 4 hours, 25 %of the original atoms will have decayed  .

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