# A radioactive nucleus can decay by three different processes simultaneously. The half life for the processes are $$1h, \dfrac {1}{\sqrt {2}}h, \dfrac {1}{2}h$$. The effective half life of the nucleus is

**A**

$$\left (1 + \dfrac {1}{\sqrt {2}} + \dfrac {1}{2}\right ) hour$$

**C**

$$\left (\dfrac {3 - \sqrt {2}}{7}\right )hour$$

**D**

$$\dfrac {1}{2\sqrt {2}} hour$$

**E**

$$\dfrac {3 + \sqrt {2}}{7} hour$$

#### Correct option is B. $$\left (\dfrac {3 - \sqrt {2}}{7}\right )hour$$