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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

Respuesta :

asuwafohjames

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'([tex]2^{T/n} [/tex])................ 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([tex]2^{T/12.3} [/tex])

Solve for T.

  • [tex]2^{T/12.3} [/tex] = 88/11
  • [tex]2^{T/12.3} [/tex] = 8
  • [tex]2^{T/12.3} [/tex] = 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

Learn more about half-life here: https://brainly.com/question/11152793

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