Natural radioactivity is a spontaneous and self disruptive activity exhibated by a number of heavy elements in nature. Thus a heavy element disintegrates by itself without being forced by any external agent to do so. According to radioactive decay law, the number of atoms disintegrated per second (i.e., rate of disintegration of radioactive atoms) at any instant is directly propotional to the number of radioactive atoms actually in the sample at that instant, i.e., `-(dN)/(dt) propN or R=-(dN)/(dt)=lambdaN`, where `lambda` is decay constant. Read the above passage and answer the following questions:
(i) The count rate form a radioactive sample containing `10^(16)` atoms is `4xx10^(6)` per second. What is the value of decay constant?
(ii) Name the three types of radiactive radiations. Which one of them is most penetrating?
(iii) What does radioactive decay law imply in day to day life?

Explanation

Let's solve the questions step by step.

### Given:
- Total number of atoms, \( N = 10^{16} \)
- Count rate (R) = \( 4 \times 10^6 \) disintegrations per second

### (i) Finding the decay constant (\( \lambda \))

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