Question

More accurate dates of the reigns of ancient Egyptian pharaohs have been determined recently using plants

Answer 1

King Tut's reign came to an end at 3350 years ago

Further explanation

Carbon-14 is a radioactive isotope that can decay. This isotope can be used to determine how long ago an organism died by knowing the ratio from 12C to 14C

Can be formulated

$\tt Nt=No\dfrac{1}{2}^{t/t1/2}$

Or we can use :

$t=-\frac{1}{\lambda }\text{ln}\left(\frac{{N}_{t}}{{N}_{0}}\right)\longrightarrow t=-\frac{1}{\lambda }\text{ln}\left(\frac{{\text{Rate}}_{t}}{{\text{Rate}}_{0}}\right)$

The half-life of C-14, 5730 years, so the decay constant :

$\tt \lambda =\dfrac{\text{ln 2}}{{t}_{1\text{/}2}}=\dfrac{0.693}{\text{5730 y}}=1.21\times {10}^{-4}}$

Assume the initial C-14 activity was 13.6  disintegrations/min/g of C

$\tt t=-\dfrac{1}{\lambda }\text{ln}\left(\dfrac{{\text{Rate}}_{t}}{{\text{Rate}}_{0}}\right)=-\dfrac{1}{1.21\times {10}^{-4}}\text{ln}\left(\dfrac{9.07}{13.6}\right)=\text{3348}\approx 3350~y$