A 96gram of sample of radioactive nuclide is placed in a container after 12min only 6gm of sample is undecayed .what is the half life of radioactive nuclide a)8hr b) 6hr c) 3hr?

1 Answer
Mar 27, 2018

See the explanation below.

Explanation:

Initial mass of nuclide is #m_0=96g#

Final mass of nuclide is #m_(12)=6g#

The time is #t=12mn#

The equation for the radioactive decay is

#m_(t)=m_0e^(-lambdat)#

Where #lambda# is the radioactive constant

Therefore,

#6=96*e^(-12lambda)#

#e^(12lambda)=96/6=16#

#12lambda=ln16=4ln2#

#lambda=1/3ln2#

But,

#lambda=ln2/t_(1/2)#

Therefore,

#t_(1/2)=ln2/lambda=ln2/(1/3ln2)=3mn#

The half life is #=3mn# and this does not fit the options given.