Chapter U1, Problem 12STP

Interpretation Introduction

Interpretation:

The approximate half life of carbon -14 needs to be calculated by using the given graph.

Concept introduction:

Half Life (t_1/2) of Carbon is defined as the time required reducing the half of the initial value of the sample.

The Half - life formula is as follows:

$N\left(t\right)=N_0{\left(\frac{1}{2}\right)}^{\frac{t}{{}^{t1/2}}}$

Where, N(t) = quantity of the substance remaining

N₀ = initial quantity of the substance

t = time lapsed

t_1/2 = Half life of the substance

Answer to Problem 12STP

Correct Option: (B) 5730 years.

Explanation of Solution

The mass of carbon-14 in sample is given by following relation:

$m\left(t\right)=100e^{-0.000121t}$

At half-life time, the mass becomes half of the initial value that is 50.

Thus,

$50=100e^{-0.000121t}$

Also,

$100e^{-0.000121t} =\frac{1}{2}$

Or,

$t=\frac{lo{g}_e\frac{1}{2}}{-0.000121}=5727.27 years\approx 5730 years$

Thus, half life of carbon-14 = 5730 years