# The half-life of carbon-14 is 5700 years. What is the age to the nearest year of a sample in which 39% of the radioactive nuclei originally present have decayed?

The sample is approximately

It is recommended to apply the half-life formula, which can be written as follows, when answering questions about half lives:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the age of the sample, you can use the formula for radioactive decay:

[ N_t = N_0 \times (1/2)^{t/T} ]

Where:

- ( N_t ) = the amount of substance remaining after time t
- ( N_0 ) = the initial amount of substance
- ( t ) = time elapsed
- ( T ) = half-life

Rearrange the formula to solve for ( t ):

[ t = \frac{T \times \log_2(N_t/N_0)}{\log_2(1/2)} ]

Given:

- ( T = 5700 ) years
- ( N_t/N_0 = 0.39 )

Substitute the values and solve for ( t ).

By signing up, you agree to our Terms of Service and Privacy Policy

- Is water used to moderate (slow down) neutrons in a nuclear reactor?
- What is the product element (isotope) produced when protactinium undergoes alpha decay?
- Could you explain me the Rutherford alpha particle scattering experiment?
- Why do alpha and beta decay produce new elements but gamma decay does not?
- Why is positron emission important?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7