What is the half-life period of a radioactive material if its activity drops to 1/16 th of its initial value in 30 years?
- 9.5 years
- 8.5 years
- 7.5 years
- 10.5 years
The Correct Option is C
Solution and Explanation
The correct answer is (C) : 7.5 years
\(∵A=\frac{A0}{\frac{t}{2^{T_{1/2}}}}\)
\(⇒2^{\frac{t}{T_{1/2}}}\)
\(=\frac{A_0}{A}=16\)
\(⇒\frac{t}{T_{1/2}}=4\)
\(⇒\frac{30}{T_{1/2}}=4\)
\(⇒T_{1/2}=\frac{30}{4}\)
=7.5 years
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Concepts Used:
Radioactivity
Radioactivity is a phenomenon observed in certain elements where unstable atomic nuclei spontaneously emit energy and subatomic particles. This process is driven by the desire of the nucleus to achieve a more stable state. It's crucial to understand the three main types of radioactive decay:
Alpha Decay: In alpha decay, a nucleus emits an alpha particle, consisting of two protons and two neutrons.
Beta Decay: Beta decay involves the emission of a beta particle, which can be a positron or an electron, from an unstable nucleus.
Gamma Decay: Gamma decay releases gamma rays, electromagnetic radiation, to achieve a more stable nuclear state.
The emission of these particles and energy is a result of nuclear instability. The rate of decay is characterized by the half-life, the time taken for half of the radioactive material to undergo decay. Radioactivity has diverse applications, from medical treatments and industrial processes to power generation in nuclear reactors.