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3 years ago

Suppose that 1 kg of Sodium-24 is reduced to 0.0156 kg in 90 hours. What is the half-life, in hours, of Sodium-24?

Mathematics

1 answer:

N76 [4]3 years ago

7 0

Answer:

14.99 hours

Step-by-step explanation:

The formula for half-life is given as,

R/R' = 2ᵃ/ᵇ...................... Equation 1

Where R= Original mass of sodium-24, R' = mass of Sodium-24 after disintegration, a = Total time taken for sodium-24 to disintegrate, b = half-life of sodiun-24.

Given: R = 1 kg, R' = 0.0156 kg, a = 90 hours

Substitute into equation 1 and solve for b

1/(0.0156) = 2⁹⁰/ᵇ

Taking the log of both side

log[1/(0.0156)] = log(2⁹⁰/ᵇ)

log[1/(0.0156)] = 90/b(log2)

90/b = log[1/(0.0156)]/log2

90/b = 6.0023

b = 90/6.0023

b = 14.99 hours

b = 14.99 hours.

Hence the half-life of Sodium-24 is 14.99 hours

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Suppose that 1 kg of Sodium-24 is reduced to 0.0156 kg in 90 hours. What is the half-life, in hours, of Sodium-24?​

Suppose that 1 kg of Sodium-24 is reduced to 0.0156 kg in 90 hours. What is the half-life, in hours, of Sodium-24?