After 42 days a 2.0 g sample of phosphorus-32 contains only 0.25 g of the isotope. What is the half-life of phosphorus-32?

2 Answers
May 13, 2018

Answer:

14 days

Explanation:

Mass of atoms initially,#N_0#=2.0 g
Mass after 42 days,#N#=0.25 g #i.e# mass left undecayed
we have,
#N/N_0=1/2^n#, where #n# is number of half lives occured(the number of times it disintegrated into half of original)
#=>0.25/2=1/2^n#
#=>1/8=1/2^n#
#=>n=3#
#=>#number of half lives occured in 42 days is 3
if half life is #t_(1/2)#
then #3t_(1/2)=42#
or #t_(1/2)=14#
#:.#half life is of 14 days

May 13, 2018

Answer:

The half life is #=14 " days "#

Explanation:

chemwiki.ucdavis.edu

The proportion of # " Phosphorus- 32 "# remaining after #42# days is

#=m_t/m_0=0.25/2=1/8#

This represents

#=3# half lives

#42# days represent #3*t_(1/2)#

Therefore,

#3*t_(1/2)=42#

#t_(1/2)=42/3=14 " days "#

The half life is #t_(1/2)=14 "days"#