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jeyben [28]
3 years ago
6

After decaying for 48 hours, one-sixteenth (1/16) of the original mass of a radioisotope sample remains unchanged. What is the h

alf-life of this radioisotope?
Chemistry
1 answer:
Hunter-Best [27]3 years ago
7 0

The half-life of this radioisotope : 12 hr

<h3>Further explanation </h3>

The atomic nucleus can experience decay into 2 particles or more due to the instability of its atomic nucleus.  

Usually radioactive elements have an unstable atomic nucleus.  

General formulas used in decay:  

\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{t/t\frac{1}{2} }}}

t = duration of decay  

t 1/2 = half-life  

N₀ = the number of initial radioactive atoms  

Nt = the number of radioactive atoms left after decaying during T time  

t=48 hr

\tt \dfrac{Nt}{No}=\dfrac{1}{16}

The half-life :

\tt \dfrac{1}{16}=\dfrac{1}{2}^{(48/t\frac{1}{2} )}\\\\(\dfrac{1}{2})^4=(\dfrac{1}{2})^{48/t\frac{1}{2}}\\\\4=48/t\frac{1}{2}\\\\t\frac{1}{2}=12~hr

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In this case, since the normal boiling point of X is 117.80 °C, the boiling point elevation constant is 1.48 °C*kg*mol⁻¹, the mass of X is 100 g and the boiling point of the mixture of X and KBr boils at 119.3 °C, we can use the following formula:

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