The ceramic glaze on a red-orange Fiestaware plate is U2O3 and contains 50.1 grams of 238U, but very little 235U. (a) What is the activity of the plate (in Ci)

The correct answer is 1.68 × 10⁻⁵ Ci

Explanation:

The activity of the uranium is determined by using the formula,  

R = 0.693 N/t1/2 (i)

The number of atoms is, N = nNA

Here, NA is the Avogadro number and n is the number of moles. The value of n is m/M, that is, mass/molecular mass. Now the value of N becomes,  

N = (m/M) NA

The m or mass of uranium given is 50.1 grams, and the molecular mass is 238 g/mol, now putting the values we get,  

N = (50 g/238 g) (6.023 × 10²³) = 1.26 × 10²³

The half-life of 238U from year to second is,  

t1/2 = (4.468 × 10⁸ year) (3.16 × 10⁷ s/ 1 year) = 1.412 × 10¹⁶ s

Substituting the values of t1/2 as 1.412 × 10¹⁶, and 1.26 × 10²³ for N in equation (i) we get,  

R = 0.639 (1.26 × 10²³) / 1.412 × 10¹⁶ s  

= 6.18 × 10⁶ Bq (2.7027 × 10⁻¹¹ Ci/1 Bq)

= 1.68 × 10⁻⁵ Ci

Hence, the activity of the plate is 1.68 × 10⁻⁵ Ci