Question 31.20: The isotope 7^16 N decays with a half-life of 7.4 s. a Calcu...

The isotope  ^{16} _{7}N decays with a half-life of 7.4 s.

a Calculate the decay constant for this nuclide.

b A sample of   ^{16} _{7}N initially contains 5000 nuclei. Determine how many will remain after a time of:

i 14.8 s                                              ii 20.0 s

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a Decay constant λ = \frac{0.693}{7.4} = 0.094  s^{–1}
b i N = N_{0}  e^{–λt} = 5.0 × 10^{3} × e^{(–0.094  ×  14.8)} = 1250
ii N = N_{0}  e^{–λt} = 5.0 × 10^{3} × e^{(–0.094  ×  20.0)} = 760 (approximately)

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