   Chapter 19, Problem 34E

Chapter
Section
Textbook Problem

# Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32 is left from an original sample of 175 mg Na332PO4 after 35.0 days? Assume the atomic mass of 32P is 32.0 u.

Interpretation Introduction

Interpretation: Half-life of phosphorus- 32 and the mass of a sample of Na332PO4 is given. By using these values, the mass of phosphorus left after 35.0 days is to be calculated.

Concept introduction: In radioactive decay, the decomposition of a parent nuclide takes place and a new daughter nuclide is formed. Phosphorus- 32 is a commonly used radioactive nuclide in biochemical research.

To determine: The mass of phosphorus left from an original sample of Na332PO4 , of the given mass, after 35.0 days.

Explanation

Explanation

Given

The value of t1/2 is 14.3days .

Mass of the sample is 175mg .

The decay time is 35.0days .

The decay constant is calculated by the formula,

k=0.693t1/2

λ=0.693t1/2

Where,

• t1/2 is the half-life of nuclide.
• k is the decay constant.

Substitute the value of half life in the above formula.

k=0.69314.3days-1=0.0484days-1_ .

The decay constant is 0.0484days-1 .

Explanation

Mass of Na332PO4 left after 35 days is calculated by the formula,

ln(NN0)=kt

Where,

• N0 is the original mass of Na332PO4 .
• N is the mass of Na332PO4 left after 35 days.
• t is the decay time.

Substitute the values of t , N0 and k in the above equation.

ln(N175mg)=0

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