Question

A radioactive nuclide has a half-life of 30.7 y. What fraction of an initially pure sample of this nuclide will remain undecayed at the end of 86.8 y?

Answer #1

**STEPS : 1- WE NEED TO CALCULATE DECAY CONSTANT
λ**

**2- WITH λ WE CAN CALCULATE REAMING RADIOACTIVE
MATERIAL **

**FORMULA: half-life t _{1/2}=ln2 /λ (λ is the
decay constant )**

**so λ=ln2/t _{1/2} (t_{1/2} given = 30.7
years)**

**λ= 0.693/30.7 = 0.02257**

**NOW N _{t} =
N_{0}e^{−λt}**

**N _{0} is the initial quantity**

**N**_{t}
** is the remaining quantity after time, t
t _{1/2} is the half-life
t time (given 86.8year)
λ is the decay constant**

** N _{t}
/N_{0}=e^{−λt}**

** N _{t}
/N_{0}=e^{−(.02257 X
86.8)}**

**N _{t}
/N_{0}=e^{−(.02257 X
86.8)}**

**N _{t}
/N_{0}=0.140**

** N _{t} =0.1410
No**

**14.10
% will remain after 86.6
years.**

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