**Question 11: In what ways is the time constant RC similar to and different from (a) Radioactive decay constant (b) Radioactive half-life?**

**ANSWER**

The decay of charge on a capacitor is given by q = q_{0}e^{-t/RC}. Here RC is the decay constant.

The decay of a radioactive substance is given by N = N_{0}e^{-λt}. Here λ is the decay constant.

#### Similarities

- Both quantities have an exponential change. Hence the curve of charge against time in capacitor has the same shape as the decay of radioactive nuclei against time.
- In the same intervals of time, the decay ratios in both processes is same.

#### Differences

- Time constant is the duration of time after which 37% charge remains on the capacitor. The decay constant λ is the rate of disintegration per nucleus.
- The unit of time constant is second (s). The unit of decay constant is per second (s
^{-1}).

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not fully given

saYes. However a fully explained answer might include some advanced level mathematics. That may be out of the scope of the question. If you are a student of second year, be contented with it. Otherwise, you can find a lot of stuff on the subject together with the exponential functions in mathematics. Thank you so much.

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