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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Atomic Physics

NTA Abhyas 2020 · Physics · Atomic Physics

A radioactive sample at some instant has a disintegration rate of...

A radioactive sample at some instant has a disintegration rate of 50005000 disintegrations per minute. After 55 minutes, the rate becomes 12501250& disintegrations per minute. Then, the decay constant (per minute) is

Options

  1. A\text{0.4} \text\ln 2
  2. B\text{0.2} \text\ln 2
  3. C\text{0.1} \text\ln 2
  4. D\text{0.8} \text\ln 2

Correct answer

A. \text{0.4} \text\ln 2

Step-by-step solution

AA0=12505000=14=(12)tT\dfrac{\text{A}}{{A}_{0}} = \dfrac{1 2 5 0}{5 0 0 0} = \dfrac{1}{4} = \left(\dfrac{1}{2}\right) \dfrac{\text{t}}{\text{T}}

⇒T=t2=52⇒ \text{T} = \dfrac{\text{t}}{2} = \dfrac{\text{5} }{2}

\lambda = \dfrac{\text\ln2}{T} = \dfrac{2}{5}l\text{n}2

=0.4ln⁡2= \text{0.4}\ln 2
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