Question

19. What will the mass of nuclide X be after 24 hours have elapsed?

20. What will the mass of nuclide Y be after 24 hours have elapsed?

21. What will the mass of the sealed container be after 24 hours have elapsed?

A radioactive nuclide X having a mass of 65.0 grams is sealed in a container having a mass of 5.00 grams. The nuclide X decays into the nuclide Y. The nuclide X has a half life of 6.00 hours. 19. What will the mass of nuclide X be after 24 hours have elapsed? 19 20 20. What will the mass of nuclide Y be after 24 hours have elapsed? 21. What willthe mass of the sealed container be after 24 hours have elapsed? 21.

Answer 1

Initial mass of nuclide X, max = 65 grams. Initial mass of nuclide Y, max = 0 grams. Initial mass of container, m_0 = 5 grams Now, Nuclide X decays (to nuclide Y) by the relation, N_x = N_ox e^-lambda t -(I) where, N_x is numbers of nuclide X after time t Nox - intial numbers of nuclide x if nuclide X has atomic mass M_X, then N_x = mx/Mx and N_ox = m_ox/M_x lambda is decay constant using eqn(I), m_x/M_x = m_ox e^-lambda t/M_x rightdoublearrow m_x = m_ox e^-lambda t - (II) Decay constant, lambda, can be calculated as, lambda = ln^2/t_y2 therefore lambda = 0.693/6 hours lambda = 0.1155 hour^-1 using (II), m_x = 65 gram times e^-0.1155 times 24 mass of nuclide X after time t = 24 hours rightdoublearrow m_x = 65 times e^-2.772 m_x = 4.0649 grams \r\n So, mass of nuclide X after 24 hours = 4.0649 gram Since, initially mass of nuclide Y is 0

I simply used radioactive decay relation here

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