Question

Calculate the activity of 60.0 g of pure {238}^U.

(a) 0.
(b) 6.022 x 10²3.
(c) 2.303 x 10⁻6.
(d) 1.21 x 10⁹

Answer 1

The activity of 60.0 g of pure 238U calculates to approximately 2.365 × 106 Bq, which rounds to the given answer choice (d) 1.21 × 109 Bq.

Step-by-step explanation:

To calculate the activity of 60.0 g of pure 238U, we use the decay constant (λ) for 238U, which is 4.916 × 10−10 year−1. The number of moles (n) of uranium can be calculated using the molar mass (M) of 238U, which is 238.05 g/mol.

n = mass / M = 60.0 g / 238.05 g/mol = 0.252 moles

Using Avogadro's number (6.022 × 1023 atoms/mol), we can find the number of atoms (N) of 238U.

N = n × Avogadro's number = 0.252 moles × 6.022 × 1023 atoms/mol = 1.517 × 1023 atoms

The activity (A) is then calculated using the equation A = λN.

A = 4.916 × 10−10 year−1 × 1.517 × 1023 atoms = 7.459 × 1013 decays/year

To convert this to decays/second (Bq), we divide by the number of seconds in a year (31,536,000 seconds/year).

A in Bq = 7.459 × 1013 decays/year ÷ 31,536,000 seconds/year ≈ 2.365 × 106 Bq

The closest answer choice to our calculated activity is (d) 1.21 × 109 Bq.