The half-life of a substance is 100 years. What the rate of decay per annum, expressed as a percentage correct to 1 decimal place?

Question

I have made an equation where

#x# is the original amount of substance
#r# is the rate of decay per anunum

#x/2# = #x (1 - r)^100#

Can someone help me solve it?

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Answer 1 · 2018-02-28T09:29:35

The rate of decay p.a is #=0.7%#

The equation for the radioactive decay is

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

The initial mass is #m_0kg#

The half life is #t_(1/2)=100y#

The radioactive constant is

#lambda=ln2/t_(1/2)=ln2/100#

Therefore,

#(m(t))/m_0=e^(-lambdat)#

#m_0/(m(t))=e^(lambdat)#

#lambdat=ln(m_0/(m(t)))#

The time is #t=1y#

Therefore,

#ln(m_0/(m(t)))=ln2/100*1#

#m_0/(m(t))=e^(ln2/100)#

#(m(t=1y))/m_0=0.993=0.993*100=99.3%#

The rate of decay p.a is #=0.7%#