The half life of a radioactive substance is 5 years. After x years, a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ______.
Correct Answer: 20
Solution and Explanation
The correct answer is 20
N = N0e–λt
\(⇒ \frac{6.25}{100} = e^{-λt}\)
\(⇒ e^{-λt} = \frac{1}{16} = (\frac{1}{2})^4\)
⇒ t = 4t1/2
⇒ t = 20 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.