The half-life of cobalt-60 is 5.26 years. If 50 g are left after 15.8 years, how many grams were in the original sample?

1 Answer
Jul 3, 2016

Answer:

#m_i= 400 \ grams#

Explanation:

The following formula relates the mass remaining of the radioiosotope to the original mass:

#m_i=m_rxx2^n#

Where:

#m_i : " is the initial mass of the radioisotope"#
#m_r: " is the mass remaining of the radioisotope after n periods"#
#n :" is the number of periods"#
# n =( "time")/ ("half life" )#

First, find the number of periods.

#n= (15.8 " years")/(5.26 " years")#
# n = 3#
Then plug in the values in the original formula

#m_i=m_rxx2^n#
#m_i = 50 xx 2^3#
#m_i= 400 \ grams#

#-------------------#

A quick approach

Knowing that the time represents three periods

# 50 -> 100 -> 200 -> 400 \ grams#