The half life of Uranium-238 against alpha decay is 4.5*10^9 years.Calculate the number of disintegrations taking place in 1gm of the substance.
1.23 * 10^4 per sec
To calculate the number of disintegrations taking place in 1 gram of Uranium-238, we will use the formula:
Number of disintegrations = (Avogadro's number * mass of substance in grams) / (atomic mass * half-life)
First, we need to find the atomic mass of Uranium-238. The atomic mass of Uranium-238 is 238 grams/mol.
Using Avogadro's number, which is approximately 6.022 x 10^23, we can proceed with the calculation:
Number of disintegrations = (6.022 x 10^23 * 1 gram) / (238 grams/mol * 4.5 x 10^9 years)
First, we need to convert years into seconds, as the unit for the half-life should match the unit of time for the calculation. There are approximately 3.1536 x 10^7 seconds in a year.
Number of disintegrations = (6.022 x 10^23 * 1 gram) / (238 grams/mol * 4.5 x 10^9 years * 3.1536 x 10^7 seconds/year)
Number of disintegrations = (6.022 x 10^23 * 1 gram) / (238 grams/mol * 4.5 x 10^9* 3.1536 x 10^7 seconds)
Now let's calculate the value:
Number of disintegrations ≈ 1.51 x 10^10 disintegrations
Therefore, in 1 gram of Uranium-238, approximately 1.51 x 10^10 disintegrations would take place.