The half-life of carbon-14 is 5370 years. the carbon-14 levels in a fossil indicate that 6 half-lives have passed. how old is the fossil?

32,220 years
75,200 years
50,000 years
35,000 years

35,000 years

Explanation: Radioactive process follow first order kinetics.

To calculate the rate constant, we use the formula:

Also :

where,  

a = amount of reactant left after n-half lives

= Initial amount of the reactant

n = number of half lives = 6

Putting values in above equation, we get:

The rate expression for first order kinetics is given by:

where,

k = rate constant

t = time taken for decay process

 = initial amount of the reactant

a = amount left after decay process

Putting values in above equation, we get:

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

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