A source holds 2.10 mg of ^210Po (molar mass 210 g mol^-1, half-life 138.4 days, N_A=6.022x10^23). The number of atoms that decay in the first 100 days, in units of 10^18, to two decimal places, is

JEE Advanced levelNumerical answerDifficulty 3 of 3as187

A source holds $2.10 mg$ of $X_{210} X_{2}^{2210} Po$ (molar mass $210 g mo l^{- 1}$ , half-life $138.4$ days, $N_{A} = 6.022 \times 1 0^{23}$ ). The number of atoms that decay in the first $100$ days, in units of $1 0^{18}$ , to two decimal places, is

Numerical answer type, answer in x 10^18, tolerance 0.02.

Atoms initially

= (2.10 \times 1 0^{- 3} /210) \times 6.022 \times 1 0^{23} = 6.022 \times 1 0^{18}

. Fraction decayed

= 1 - 2^{- 100/138.4} = 1 - 0.606 = 0.394

. Decayed atoms

= 6.022 \times 1 0^{18} \times 0.394 = 2.37 \times 1 0^{18}