Question

The half life of a radioactive element is 8 hours. A sample of the element is tested and found to contain 6g of the element. How much of the element was present 32 hours before the element was tested? 0.375g 6g 48g 96g

Answer 1

Answer:

m₀ = 96 g

Explanation:

First, we will calculate the no. of half-lives passed:

$n = \frac{T}{T_{1/2}}$

where,

n = no. of half-lives passed = ?

T = Total time elapsed = 32 h

$T_{1/2}$ = Half-Life = 8 h

Therefore,

$n = \frac{32\ h}{8\ h}\\\\n = 4$

Now, for the initial amount of element:

$m = \frac{m_o}{2^n}\\\\m_o = m(2^n)$

where,

m₀ = initial amount of element = ?

m = current amount of element = 6 g

Therefore,

$m_o = (6\ g)(2^4)$

m₀ = (6 g)(16)

m₀ = 96 g