A RADIOACTIVE NUCLEUS HAS A HALF-LIFE OF 20 YEARS, STARTING WITH 100,000 PARTICLES, HOW MANY PARTICLES WILL BE LEFT EXACTLY AT THE END OF 40 YEARS

• A. 75,000 particles
• B. 35,000 particles
• C. 25,000 particles ✓
• D. 50,000 particles

 

The answer to the question is: C. 25,000 particles

The decay of a radioactive nucleus can be described by its half-life, which is the time it takes for half of the radioactive particles to decay. In this case, the half-life of the radioactive nucleus is 20 years, and we want to determine the number of particles remaining after 40 years.

To solve this problem, we can use the exponential decay formula:

N(t) = N0 * (1/2)^(t/T)

Where:

N(t) = the number of particles remaining after time t

N0 = the initial number of particles

t = time elapsed

T = half-life

Given:

N0 = 100,000 particles

T = 20 years

t = 40 years

Plugging these values into the formula:

N(40) = 100,000 * (1/2)^(40/20)

  = 100,000 * (1/2)^2
  = 100,000 * (1/4)
  = 25,000 particles

Therefore, at the end of 40 years, there will be exactly 25,000 particles left