Question

In a radioactive decay, the fraction of the number of atoms left undecayed after time \( t \) is:

• A. \( e^{-\lambda t+1} \)
• B. \( e^{-\lambda t} \)
• C. \( e^{\lambda t} \)
• D. \( e^{\lambda t-1} \)
• E. \( e^{t+1} \)

Hint:

The exponential decay law governs the decrease in the number of radioactive atoms over time.

Answer 1

The Correct Option is B

The radioactive decay law states that the number of undecayed atoms decreases exponentially over time. 
The fraction of undecayed atoms at time \( t \) is given by: \[ N(t) = N_0 e^{-\lambda t} \] where: 
- \( N_0 \) is the initial number of atoms, 
- \( \lambda \) is the decay constant, 
- \( t \) is the time elapsed. 
Since the decay follows an exponential pattern, the correct answer is \( e^{-\lambda t} \).