# Calculating Radioactive Decay: Number of Disintegrations per Second

## How to calculate the number of disintegration per second in 1g of ²³⁸U?

Given that the half-life of ²³⁸U for α-decay is 4.5×10⁹ years, we need to determine the number of disintegrations per second.

## Answer:

The correct answer is (b) 1.325 x 10⁴s⁻¹.

To calculate the number of disintegrations per second in 1g of ²³⁸U, we can use the formula:

R = A * N_A / M

- R = number of disintegrations per second
- A = activity of ²³⁸U
- N_A = Avogadro's number (6.023 10²³ mol⁻¹)
- M = molar mass of ²³⁸U

Plugging in the values given in the question:

R = 4.51x10^16 * 6.023x10^23 / 238 = 1.325x10^4s⁻¹

Therefore, the correct answer is (b) 1.325 x 10⁴s⁻¹.