Question

Although most natural potassium nuclei are stable 39K (93.3%) or 41K (6.7%) nuclei, about 0.0117% are radioactive 40K nuclei, which have a half-life of 1.26 billion years. What fraction of all the potassium nuclei in your body will undergo radioactive decay in the next 0.57-year period?

fraction=

(answer to the 4th decimal point without rounding. cant answer with x10 anything)

Answer 1

LET TE NUMBER OF K₄₀ NUCLEI BE N

ACTIVITY , A = N Ln2 / decays / sec

A = N ln 2 /(1.26 x10⁹ * 365* 24 * 3600) per sec

for 0.57 years decay is = ( N ln 2 *0.57 * 365* 24 * 3600)  /(1.26 x10⁹ * 365* 24 * 3600)

= 0.31356 * 10^-9 N decay

percentage of k₄₀ that decays in 0.57 years = 0.31356 * 10^-9 N * 100 / N = 0.31356 * 10^-7 % o

percentage of total pottassium in our body = 0.31356 * 10^-7 % * 0.0117 %* of total pottassium

= 3.668 * 10^-12 %

so the answer is = 0.0000 as asked in question