Polonium-214 has a relatively short half life of 164 s. How many seconds would it take for 8.0 g of this isotope to decay to 0.25 g?

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Answer 1 · 2016-06-05T07:01:28

# 820 \ sec#

#m_i=m_r*2^n#

#m_i " is the initial mass present of the radioisotope."#

#m_r" is the mass remaining after a certain time "#

#n " is the number of periods," = (time)/T" where T is the half-life."#

#m_i=m_r*2^n#

#m_i/m_r=2^n#

#2^n=(8.0\ g)/(0.25\ g)#

#2^n=32#

#2^n=2^5 " " => # n = 5

#n= (time)/T#

# time = n xx T#

# time = 5 xx 164 \ sec#

# time = 820 \ sec#

A quick approach:

# underbrace(8\ g -> 4 \ g->2\ g->1\ g ->0.5 \ g-> 0.25 g)#
# " "Time#

# Time = 5 \ periods# ...