Isotope Decay and Mass Calculations

The video tutorial explains how to calculate the remaining mass of an alien isotope with a half-life of 238 years from an initial 8 kg sample after 100 years. It involves calculating the decay constant K using the natural logarithm of 2 divided by the half-life, formulating the decay function, and then using this function to find the remaining mass. The final result shows that approximately 6 kg of the isotope remains after 100 years.

What is the half-life of the alien isotope mentioned in the problem?

• 500 years

• 50 years

• 238 years

• 100 years

What is the initial mass of the isotope sample?

• 12 kg

• 8 kg

• 10 kg

• 5 kg

Which mathematical function is used to calculate the decay constant (K)?

• Exponential

• Polynomial

• Logarithmic

• Trigonometric

What is the formula to calculate the decay constant (K)?

• K = half-life * ln(2)

• K = half-life / ln(2)

• K = ln(2) * half-life

• K = ln(2) / half-life

To how many decimal places should the decay constant be rounded?

• Two

• Five

• Three

• Four

What is the decay constant (K) rounded to four decimal places?

• -0.0031

• -0.0029

• -0.0030

• -0.0028

What is the general form of the decay function?

• A(t) = A0 * e^(Kt)

• A(t) = A0 * e^(t/K)

• A(t) = A0 * e^(-Kt)

• A(t) = A0 * e^(K/t)

What does 'A0' represent in the decay function?

• Decay constant

• Final amount

• Initial amount

• Time

What is the time period used to calculate the remaining mass in the problem?

• 100 years

• 150 years

• 200 years

• 50 years

What is the exponent value when calculating the remaining mass after 100 years?

• -0.19

• -0.29

• -0.39

• -0.09