Initial number of not decayed nucleis 5cdot 10^10 Half-life is equal to 200 seconds. In 400 seconds the number of not decayed nuclei is equal to Bbibepute onMH orger. a. 1.25cdot 10^10 b. 2.5cdot 10^10 C. 25cdot 10^9 d. 0 e. 5cdot 10^9

The decay of nuclei follows the exponential decay law, and the number of undecayed nuclei after a certain time \( t \) can be calculated using the formula:<br /><br />\[<br />N(t) = N_0 \cdot \left(\frac{1}{2}\right)^{t/T_{1/2}}<br />\]<br /><br />Where:<br />- \( N_0 \) is the initial number of nuclei,<br />- \( T_{1/2} \) is the half-life,<br />- \( t \) is the elapsed time.<br /><br />### Given:<br />- \( N_0 = 5 \cdot 10^{10} \),<br />- \( T_{1/2} = 200 \, \text{s} \),<br />- \( t = 400 \, \text{s} \).<br /><br />Substitute these values into the formula:<br /><br />\[<br />N(400) = 5 \cdot 10^{10} \cdot \left(\frac{1}{2}\right)^{400/200}<br />\]<br /><br />Simplify the exponent:<br /><br />\[<br />\frac{400}{200} = 2<br />\]<br /><br />So:<br /><br />\[<br />N(400) = 5 \cdot 10^{10} \cdot \left(\frac{1}{2}\right)^2<br />\]<br /><br />\[<br />N(400) = 5 \cdot 10^{10} \cdot \frac{1}{4}<br />\]<br /><br />\[<br />N(400) = 1.25 \cdot 10^{10}<br />\]<br /><br />### Final Answer:<br />**a. \( 1.25 \cdot 10^{10} \)**