Question

If a radioactive substance has initial mass m₀ and half-life h , write an expression for the mass m(t) remaining at time t .

Answer 1

The expression for the mass remaining at time t in a radioactive substance with initial mass m₀ and half-life h is m(t) = m₀ * e^(-kt), where m(t) is the mass remaining at time t, m₀ is the initial mass, e is the base of the natural logarithm, k is the decay constant, t is the elapsed time, and h is the half-life of the substance.

Step-by-step explanation:

The expression for the mass remaining at time t in a radioactive substance with an initial mass m₀ and a half-life h can be written as:

m(t) = m₀ × e^(-kt)

Where:

• m(t) is the mass remaining at time t
• m₀ is the initial mass
• e is the base of the natural logarithm (~2.71828)
• k is the decay constant, given by k = ln(2) / h
• t is the elapsed time
• h is the half-life of the substance

For example, if the initial mass is 10 grams and the half-life is 5 days, the expression for the mass remaining after 3 days would be:

m(3) = 10 × e^(-ln(2)/5 × 3)