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Two radioactive sources A and B initially contain equal number of radioactive atoms. Source A has a half-life of 1 hour and source B has a half-life of 2 hours. At the end of 2 hours, the ratio of activity of source A to that of B is : 
  • a)
    1 : 2    
  • b)
    2 : 1
  • c)
    1 : 1
  • d)
    1 : 4
Correct answer is option 'C'. Can you explain this answer?
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Explanation:

To understand the ratio of activity of source A to source B, we need to first understand the concept of half-life.

Half-Life:

The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a sample to decay. It is a characteristic property of each radioactive material.

Source A:

Source A has a half-life of 1 hour. This means that after every hour, the number of radioactive atoms in source A will reduce by half.

Source B:

Source B has a half-life of 2 hours. This means that after every 2 hours, the number of radioactive atoms in source B will reduce by half.

At the end of 2 hours:

Let's assume that both sources A and B initially contain 'x' number of radioactive atoms.

After 1 hour, source A will have 'x/2' radioactive atoms remaining.
After 2 hours, source A will have 'x/4' radioactive atoms remaining.

After 2 hours, source B will have 'x/2' radioactive atoms remaining.

Ratio of activity:

The activity of a radioactive source is directly proportional to the number of radioactive atoms present. Therefore, we can compare the ratio of the remaining radioactive atoms in source A to that in source B.

At the end of 2 hours:
Activity of source A = 'x/4'
Activity of source B = 'x/2'

To find the ratio, we divide the activity of source A by the activity of source B:
('x/4') / ('x/2') = 1/2

Therefore, the ratio of activity of source A to that of source B is 1 : 2.

Answer:

The correct answer is option a) 1 : 2.
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Two radioactive sources A and B initially contain equal number of radioactive atoms. Source A has a half-life of 1 hour and source B has a half-life of 2 hours. At the end of 2 hours, the ratio of activity of source A to that of B is :a)1 : 2 b)2 : 1c)1 : 1d)1 : 4Correct answer is option 'C'. Can you explain this answer?
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