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A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per min. Then, the decay constant (per minute) is
  • a)
    0.4 ln 2
  • b)
    0.2 ln 2
  • c)
    0.1 ln 2
  • d)
    0.8 ln 2
Correct answer is option 'A'. Can you explain this answer?
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A radioactive sample at any instant has its disintegration rate 5000 d...
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A radioactive sample at any instant has its disintegration rate 5000 d...
The decay constant (λ) of a radioactive substance is a measure of its rate of decay. It is defined as the probability of a nucleus decaying per unit time. In this question, we are given the disintegration rate of a radioactive sample at two different instances and we need to find the decay constant.

Let's analyze the given information:

1. The disintegration rate at any instant is 5000 disintegrations per minute.
2. After 5 minutes, the disintegration rate is 1250 disintegrations per minute.

To find the decay constant, we can use the equation for radioactive decay:

N(t) = N₀ * e^(-λt)

Where:
N(t) is the number of radioactive nuclei at time t
N₀ is the initial number of radioactive nuclei
λ is the decay constant
t is the time

We can use the given information to set up two equations:

5000 = N₀ * e^(-λ*0)
1250 = N₀ * e^(-λ*5)

Simplifying the first equation, we get:

5000 = N₀

Substituting this value into the second equation, we get:

1250 = 5000 * e^(-λ*5)

Dividing both sides by 5000, we get:

0.25 = e^(-λ*5)

Taking the natural logarithm of both sides, we get:

ln(0.25) = -λ*5

Rearranging the equation, we get:

λ = -ln(0.25) / 5

Simplifying the equation further, we get:

λ ≈ 0.4 ln 2

Therefore, the correct answer is option A: 0.4 ln 2.
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A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per min. Then, the decay constant (per minute) isa)0.4 ln 2b)0.2 ln 2c)0.1 ln 2d)0.8 ln 2Correct answer is option 'A'. Can you explain this answer?
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A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per min. Then, the decay constant (per minute) isa)0.4 ln 2b)0.2 ln 2c)0.1 ln 2d)0.8 ln 2Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per min. Then, the decay constant (per minute) isa)0.4 ln 2b)0.2 ln 2c)0.1 ln 2d)0.8 ln 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per min. Then, the decay constant (per minute) isa)0.4 ln 2b)0.2 ln 2c)0.1 ln 2d)0.8 ln 2Correct answer is option 'A'. Can you explain this answer?.
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