A sample radio active subsistence has ${10}^6$radio active nuclei. It's half-life is 20 sec. How many nuclei will remain after 10 seconds 

The decay of radioactive nuclei follows an exponential decay law given by the equation:

$N\left(t\right)=N_0\times {\left(\frac{1}{2}\right)}^{\frac{t}{T}}$

Given: 

$N_0={10}^6$ (initial number of radioactive nuclei) 

T = 20 seconds (half-life) 

t = 10 seconds (time elapsed)

Plugging in the values into the formula:

$N\left(10\right)={10}^6\times {\left(\frac{1}{2}\right)}^{\frac{10}{20}}$

$N\left(10\right)={10}^6\times {\left(\frac{1}{2}\right)}^{0.5}$

$N\left(10\right)={10}^6\times 0.7071$

$N\left(10\right)=7.071\times {10}^5$

Rounding to the nearest integer, we get:

$N\left(10\right)\approx 7\times {10}^5$

Hence the correct answer is $7\times {10}^5.$