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# 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
$$\left (1 + \dfrac {1}{\sqrt {2}} + \dfrac {1}{2}\right ) hour$$
B
$$\dfrac {1}{2} hour$$
C
$$\left (\dfrac {3 - \sqrt {2}}{7}\right )hour$$
D
$$\dfrac {1}{2\sqrt {2}} hour$$
E
$$\dfrac {3 + \sqrt {2}}{7} hour$$
Solution
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#### Correct option is B. $$\left (\dfrac {3 - \sqrt {2}}{7}\right )hour$$

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