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-A Radioactive Isotope $\mathrm { X }$ Is a By-Product of Nuclear Fission with a Half-Life Of a By-Product

question 273

Multiple Choice

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-A radioactive isotope $\mathrm { X }$ is a by-product of nuclear fission with a half-life of $28.7 \mathrm { yr }$ . After a nuclear accident, large areas surrounding the site were contaminated with isotope X. If 10 micrograms of $X$ is present in a sample, the function $A ( t ) = 10 \left( \frac { 1 } { 2 } \right) ^ { t / 28.7 }$ gives the amount $A ( t )$ , in micrograms, present after $t$ years. Evaluate the function for the given values of $t$ and interpret the meaning in context.
a. $A ( 57.4 ) \quad$ b. $A ( 100 )$

• A) a. After \(57.4\) years the amount of isotope \(X\) is \(2.5 \mu \mathrm { g }\).
• b. After 100 years the amount of isotope \(X\) is approximately \(1.138 \mu \mathrm { g }\).
• B) a. After \(57.4\) years the amount of isotope \(X\) is \(5 \mu \mathrm { g }\).
• b. After 100 years the amount of isotope \(X\) is approximately \(1.138 \mu \mathrm { g }\).
• C) a. After \(57.4\) years the amount of isotope \(X\) is \(5 \mu \mathrm { g }\).
• b. After 100 years the amount of isotope \(X\) is approximately \(0.894 \mu \mathrm { g }\).
• D) a. After \(57.4\) years the amount of isotope \(X\) is \(2.5 \mu \mathrm { g }\).
• b. After 100 years the amount of isotope \(\mathrm { X }\) is approximately \(0.894 \mu \mathrm { g }\).

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Definitions:

Hair Cells

Sensory cells found in the inner ear that translate sound vibrations into electrical signals for the brain to interpret as sound.

Action Potential

An electrical impulse in neurons, resulting from the movement of ions across the cell membrane, crucial for nerve signal transmission.

Pacinian Corpuscles

Specialized nerve endings in the skin and viscera that detect mechanical pressure or vibrations.

Statocysts

Sensory organs found in some aquatic invertebrates, such as crustaceans and mollusks, used to sense gravity and enable balance and orientation.