Final answer:
To calculate the values of K and t after one week, we can use the equation: K = K₀ * e^(-λt), where K₀ is the initial flux density, λ is the decay constant, t is the time in seconds, and e is the base of the natural logarithm.
Step-by-step explanation:
The flux density of 6-MeV y-rays is 3.4 X 10⁶/cm²s at a point in Pb. To calculate the values of K and t after one week, we can use the equation: K = K₀ * e^(-λt), where K₀ is the initial flux density, λ is the decay constant, t is the time in seconds, and e is the base of the natural logarithm.
First, let's calculate the decay constant using the half-life formula: T₁/₂ = ln(2) / λ, where T₁/₂ is the half-life. For 6-MeV y-rays, the half-life is 47.5 hours or 171000 seconds.
Substituting the values into the equation, we have: K = 3.4 X 10⁶ * e^(-ln(2) * t / 171000). After one week (7 days or 604800 seconds), the value of K will be: K = 3.4 X 10⁶ * e^(-ln(2) * 604800 / 171000).