Question

sodium-24 has a half-life of 15 hours. how many grams of a 900 g sample will remain after 90 hours
A.28.125g
B.14.0625 g
C.7.5 g
D.7.03125 g

Answer 1

Answer: Option 'B' is correct.

Step-by-step explanation:

Let the initial concentration be

$N_0=900\ g$

Let concentration after t= 90 hours be N

Since we have given that Sodium-24 has a half life of 15 hours i.e.

$t_{\frac{1}{2}}=15$

So, According to question,

$\text{ Number of half lives }=\frac{t}{t_{\frac{1}{2}}}\\\\\text{ Number of half lives }=\frac{90}{15}\\\\\text{ Number of half lives }=6$

As we know that

$\frac{N}{N_0}=(\frac{1}{2})^n\\\\N=N_0\times (\frac{1}{2})^n\\\\N=900\times (\frac{1}{2})^6\\\\N=\frac{900}{64}\\\\N=14.0625\ g$

Hence, Option 'B' is correct.