Half life of radium is 44 years.The sample will reduce to 50% of its orignal value after how many years?
44 years
I have confusion regarding this question that in one of my book its answer is 44year while in other its answer is 22 year.
please help.
Faryal ilyas
To calculate the time it takes for a sample of radium to reduce to 50% of its original value, we need to use the concept of half-life.
The half-life is the time it takes for half of the radioactive atoms in a substance to decay. In this case, the half-life of radium is given as 44 years, which means that after 44 years, half of the radium atoms in a sample will have decayed.
To find the time it takes for the sample to reduce to 50% of its original value, we need to calculate how many half-lives have elapsed. Since each half-life reduces the sample by half, we need to determine the number of times we can divide the sample size by 2 until we reach 50%.
Let's do the calculation:
1st half-life: 50% of the original value
2nd half-life: 25% of the original value
3rd half-life: 12.5% of the original value
4th half-life: 6.25% of the original value
By the 4th half-life, the sample has reduced to 6.25% of its original value. We can notice that after the 3rd half-life, the value is still above 50%.
Therefore, we can conclude that it takes 4 half-lives for the sample to reduce to 50% of its original value. Since the half-life of radium is 44 years, multiply 44 years by 4 to get the answer.
44 years * 4 = 176 years
So, the sample will reduce to 50% of its original value after approximately 176 years.