Answer :
It will take 6.6hours for 85% of the lead for radioactive decay
What is radioactive decay?
Radioactive decay is the emission of power withinside the shape of ionizing radiation. The ionizing radiation this is emitted can include alpha particles, beta particles and/or gamma rays. Radioactive decay happens in unbalanced atoms known as radionuclides.
Elements withinside the periodic desk can tackle numerous bureaucracy. Some of those bureaucracy are strong; other kinds are risky. Typically, the maximum strong shape of an detail is the maximum not unusual place in nature. However, all factors have an risky shape. Unstable bureaucracy emit ionizing radiation and are radioactive. There are a few factors without a strong shape which are constantly radioactive, together with uranium. Elements that emit ionizing radiation are known as radionuclides.
[tex]\frac{dN}{dt} = -\lambda N\\ \\ \implies N = N_0e^{-\lambda t}[/tex]
Since, initial amount was 1g,
[tex]N = (1)e^{-\lambda t} = e^{-\lambda t}[/tex]
Half life is 3.3 hours. So,
[tex]\frac{1}{2} = e^{-\lambda (3.3)} \implies \lambda = \frac{\ln2}{3.3}[/tex]
SO, after 75% decay, only 25% is left. So,
[tex]\frac{1}{4} = e^{-\frac{\ln2}{3.3}t} \implies t = 6.6 \ \text{hours}[/tex]
It will take 6.6hours for 85% of the lead for radioactive decay
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