Question

Hydrogen-3 has a half-life of 12.3 years. How long will it take a sample of 88 g of hydrogen-3 to decay to 11 g? Give your answer to three significant digits. ____

years

Answer 1

The time taken for Hydrogen-3 to decay from 88 g to 11 g is 36.9 years.

Half-life:

This can be defined as the time taken for half the sample of a substance to decay or disintegrate

To calculate the time it will take Hydrogen to decay from 88g to 11 g we use the formula below.

Formula:

• R = R'($2^{T/n}$)................ Equation 1

Where:

• R = Original sample of Hydrogen
• R' = Sample of Hydrogen left after decay
• T = Total time of decay
• n = Half-life of hydrogen.

From the question,

Given:

• R = 88 g
• R' = 11 g
• n = 12.3 years.

Substitute these values into equation 1

• 88 = 11($2^{T/12.3}$)

Solve for T.

• $2^{T/12.3}$ = 88/11
• $2^{T/12.3}$ = 8
• $2^{T/12.3}$ = 2³................ Equation 2

Equating the base in equation 2 above,

• T/12.3 = 3
• T = 12.3×3
• T =  36.9 years.

Hence, the time taken for Hydrogen-3 to decay from 88 g to 11 g is 36.9 years

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