# NEET Physics Nuclei Questions Solved

The half-life of a sample of a radioactive substance is 1 hour. If $8×{10}^{10}$ atoms are present at t = 0, then the number of atoms decayed in the duration t = 2 hour to t = 4 hour will be
(a) $2×{10}^{10}$          (b) $1.5×{10}^{10}$
(c) Zero               (d) Infinity

(b) $\mathrm{N}={\mathrm{N}}_{0}{\left(\frac{1}{2}\right)}^{\frac{\mathrm{t}}{{\mathrm{T}}_{1/2}}}$
No of atoms at t = 2hr, ${\mathrm{N}}_{1}=8×{10}^{10}{\left(\frac{1}{2}\right)}^{\frac{2}{1}}=2×{10}^{10}$
No. of atoms at t = 4hr, ${\mathrm{N}}_{2}=8×{10}^{10}{\left(\frac{1}{2}\right)}^{\frac{4}{1}}=\frac{1}{2}×{10}^{10}$
$\therefore$ No. of atoms decayed in given duration

$=\left(2-\frac{1}{2}\right)×{10}^{10}=1.5×{10}^{10}$

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