Question:

A certain radioactive substance has a half-life of 50 years. If initially there are 8000 atoms of this substance, how many atoms will remain after 200 years?

(A) 500 atoms (B) 625 atoms (C) 1000 atoms (D) 1250 atoms

Answer:

The number of atoms remaining after a certain time can be calculated using the formula:

N = N₀ * (1/2)^(t / T)

where:

• N is the number of atoms remaining after time t
• N₀ is the initial number of atoms
• t is the time passed
• T is the half-life of the substance

Given:

• Initial number of atoms (N₀) = 8000
• Half-life (T) = 50 years
• Time passed (t) = 200 years

Plugging in the given values into the formula:

N = 8000 * (1/2)^(200 / 50)

Simplifying the exponential term:

N = 8000 * (1/2)^4

N = 8000 * (1/16)

N = 500

Therefore, after 200 years, there will be 500 atoms remaining.

Answer: (A) 500 atoms