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In a smaple of radioactive material, wha...

In a smaple of radioactive material, what fraction of the initial number of active nuclei will remain undisingrated after half of a half-life of the sample?
a. `(1)/(4)` b. `(1)/(2 sqrt(2))` c. `(1)/(sqrt(2))` d. `sqrt(2) - 1`

A

a. `(1)/(4)`

B

b. `(1)/(2 sqrt(2))`

C

c. `(1)/(sqrt(2))`

D

d. `sqrt(2) - 1`

Text Solution

Verified by Experts

The correct Answer is:
c. `(1)/(sqrt(2))`
`(0.693)/(t_(1//2)) = (2.303)/(t) log ((N_(0))/(N))`
`(2.303 xx log 2)/(t_(1//2)) = (2.303)/((t_(1//2)//2)) log_(10) ((N_(0))/(N))`
`((N)/(N_(0))) = (1)/(sqrt(2))`
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