There are `4sqrt2xx10^6` radioactive nuclei in a given radioactive sample. If half life of sample is 20s, how many nuclei will decay in 10seconds?

Explanation

Here, `N_0=4sqrt2xx10^6`,
`T=20s, t=10s`,
form `N/(N_0)=(1/2)^(t//T)=(1/2)^(10//20)=(1/2)^(1//2)=1/(sqrt2)`
`N=(N_0)/(sqrt2)=(4sqrt2)/(sqrt2)xx10^6=4xx10^6`
Number of nuclie decayed=`N_0-N`
`=4sqrt2xx10^6-4xx10^6`
`=4xx10^6(sqrt2-1)`
`=4xx0.414xx10^6=1.656xx10^6`