Question

If you had a 5 gram sample of lawrencium how much would still remain in 30 minutes

Answer 1

Answer:

$\large \boxed{\text{4.5 g}}$

Explanation:

There are eight isotopes of lawrencium, and they are all radioactive,

I will do the calculation for ²⁶²Lr, which has a half-life of 3.6 h.

Let A₀ = the original amount of lawrencium.

The amount remaining after one half-life is ½A₀.

After two half-lives, the amount remaining is ½ ×½A₀ = (½)²A₀.

After three half-lives, the amount remaining is ½ ×(½)²A₀ = (½)³A₀, and so on.

We can write a general formula for the amount remaining:

A =A₀(½)ⁿ

where n is the number of half-lives

$n = \dfrac{t}{t_{\frac{1}{2}}}$

Data:

A₀ = 5 g

  t = 30 min

$t_{\frac{1}{2}} = \text{3.6 h}$

Calculations:

(a) Convert the half-life to minutes

$t_{\frac{1}{2} }= \text{3.6 h} \times \dfrac{\text{60 min}}{\text{1 h}} = \text{216 min}$

(b) Calculate n

$n = \dfrac{30}{216} = 0.1389$

(c) Calculate A

$A = \text{5 g} \times \left (\dfrac{1}{2}\right)^{0.1389} = \text{5 g} \times 0.9082 = \textbf{4.5 g}\\\\\text{The mass of lawrencium remaining after 30 min is \large \boxed{\textbf{4.5 g}} }$