​The radioactive isotope of an element has a half-life of 100 hours. How many hours will it take for $$\frac{15}{16}$$ of the source amount to decay? ​

Correct option is B

Explanation-

Step 1: Use the formula
   Each half-life divides the remaining amount by 2:
                                                                   $$\text{Remaining fraction} = \left( \frac{1}{2} \right)^n$$

$$\left( \frac{1}{2} \right)^n = \frac{1}{16}$$

                   Now solve for :            
                                                                            $$\left( \frac{1}{2} \right)^4 = \frac{1}{16} \Rightarrow n = 4$$

So, it takes 4 half-lives for 15/16 to decay.

Step 2: Multiply by the half-life duration
                       Each half-life is 100 hours: 

                                                                     $$\text{Total time} = 4 \times 100 = \boxed{400 \text{ hours}}$$​ 

So, the correct answer is option b : 400