Question

46. (a) Calculate the activity R of 1.69 of 226Ra. (Note: A = 2 N.). Answer to 3SigFigs in Bq. Check Ch31 P59. World War Il aircraft had instruments with glowing radium-painted dials (see Figure 31.2). The activity of one such instrument was 4.0x105 Bq when new. (a) What is the initial mass of 226 Ra in grams? Enter your answer to 7SigFigs. Units are not entered for this problem. (b) After some years, the phosphors on the dials deteriorated chemically, but the radium did not escape. What is the activity of this instrument 57.0 years after it was made? Enter your answer to 3sigFigs in Bq. Units are not entered in this answer. Check

Answer 1

46.(a)

Mass of Ra-226, m = 1.6 g

Molar mass of Ra- 226, M = 226 g

Number of nuclei present in m g of Ra-226 is N = m N_A/M = 1.6 x 6.023 x 10²³/226 = 4.26 x 10²¹

Half life of Ra-226 is t_1/2 = 1600 years = 5.04 x 10¹⁰ s

Decay constant, λ = 0.693/ t_1/2 = 0.693/5.04 x 10¹⁰ = 1.38 x 10^-11 s^-1

Activity of the sample of Ra-226 is R = λ N = 1.38 x 10^-11 x 4.26 x 10²¹ = 5.88 x 10¹⁰ Bq

Activity of the sample of Ra-226 is R = 5.88 x 10¹⁰ Bq

59. (b)

Initial activity of Ra-226 is R₀ = 4.0 x 10⁵ Bq

Molar mass of Ra- 226, M = 226 g

Decay constant of Ra-226, λ = 1.38 x 10^-11 s^-1

Initial activity, R₀ = λ N₀

Initial number of atoms present, N₀ = R₀ / λ = 4.0 x 10⁵ /1.38 x 10^-11 = 2.89 x 10¹⁶

Initial mass of the sample, m₀ = M N₀ / N_A = 226 x 2.89 x 10 ¹⁶ /6.023 x 10²³ = 1.08 x 10^-5 kg = 1.08 x 10^-2 g

Initial mass of the sample, m₀ = 1.08 x 10^-2 g

( C )

Activity after t years is R = R₀ e^-λt

Decay constant, λ = 0.693/ t_1/2 = 0.693/1600 = 0.000433 year^-1

R = 4.0 x 10⁵ x e^{-0.000433 x 57} = 3.90 x 10⁵ Bq

Activity after 57 years, R = 3.90 x 10⁵ Bq