Nuclei — Practice

Question 1

A substance has a 10-day half-life. How much of a 1 g sample remains after 30 days?

Accepted Answer

30 days = 3 half-lives. Remaining = 1 x (1/2)^3 = 0.125 g.

Question 2

A sample's activity falls from 240 Bq to 30 Bq in 6 hours. Find the half-life.

Accepted Answer

240 x (1/2)^n = 30 gives (1/2)^n = 1/8, n = 3. Half-life = 6/3 = 2 hours.

Question 3

Find the energy released when 1 g of U-235 fissions (~200 MeV each).

Accepted Answer

Nuclei = (1/235) x 6.022e23 = 2.56e21. Energy = 2.56e21 x 200 x 1.6e-13 = 8.2e10 J.

Question 4

Find the binding energy of helium-4 (m_p = 1.007825, m_n = 1.008665, m_He = 4.002603 u).

Accepted Answer

delta-m = 2(1.007825) + 2(1.008665) - 4.002603 = 0.030377 u. E_b = 0.030377 x 931.5 = 28.3 MeV (BE/A = 7.07 MeV).

Question 5

A nuclide decays to 1/16 of its amount in 20 days. Find half-life and decay constant.

Accepted Answer

(1/2)^n = 1/16 gives n = 4, so half-life = 5 days. lambda = 0.693/5 = 0.139 per day.

Practice — Nuclei