In a desert cave, an artifact has been discovered. The anthropologists investigating this artifact want to determine its age. They note that the current activity level of the artifact is 9.25 decays/s, and the carbon mass present is 0.100 kg. To ascertain the artifact's age, they will employ specific constants:

r=1.2

The formula for carbon 14 activity is

$A=A_0e^{\lambda t}$

where,

$A_0$ is the initial activity of the substance

Now, solve for t

$-\lambda t=In\frac{A}{A_0}$

$t=-\frac{1}{\lambda} In(\frac{A}{A_0} )$

$=-\frac{1}{\lambda} In(\frac{A}{\lambda r(\frac{m_c}{m_a} )} )$

since,

$A_0=\lambda r(\frac{m_c}{m_a} )$

$=-\frac{1}{\lambda} In(\frac{A\ m_a}{\lambda r m_c} )$

Thus, the age of the artifact is

$=-\frac{1}{\lambda} In(\frac{A\ m_a}{\lambda r m_c} )$

$=-\frac{1}{1.21\times 10^{-4}} In(\frac{(9.25)(2.32\times 10^{-26}}{1.21\times 10^{-4}(\frac{1}{3.15569\times10^7} )(1.2\times 10^{-12})(0.100)}} )\\\\=6303.4 \ years$

to two significant figures = 6300 years

4 0

3 months ago

6.An acid-base indicator is usually a weak acid with a characteristic color in the protonated and deprotonated forms. Because br

Tems11 [2777]

Answer:

When HBCG and BCG^- are at the same concentration, the resulting color is green. This green shade initially becomes visible at a pH of 3.8.

Explanation:

HBCG serves as an indicator formed by dissolving solids in ethanol.

Since

Ka=[BCG−][H3O+][HBCG] When [BCG-] equals [HBCG], it follows that Ka = [H3O+].

<pWith a pH of 3.8,<pKa= [H3O+] = -antilog pH = -antilog (3.8)

Ka= 1.58 ×10^-4

5 0

3 months ago