Q. 5.88 - An Introduction to General, Organic, and Biological Chemistry

Question

Element 116 was recently named Livermorium, symbol L.v, The reaction for its synthesis involves bombarding Cm-248 with Ca-48. Write the balanced nuclear equation for the synthesis of livermorium. $\{5.2)$

Step-by-Step Solution

Answer

Sodium-24 has a half-life of 24 hours$15.1 \mathrm{h}$.

Step 1: Introduction

Half-time refers to the period during which the amount of sample has decayed by half. To find the half-time, start by calculating the decays constant:

$N=N_0{e}^{-2t}$ or

$InN-In{N}_0=-\lambda t$

Step 2: Explanation

Here, $N_0$ is the initial concentration of Sodium-24 is $16\mu \mathrm{g},N$ is the concentration after $45 \mathrm{h}$ is $2\mu \mathrm{g},t$ is time $45 \mathrm{h}$ and$\lambda$ is decay constant.

$In\frac{2.0}{16.0}=-\lambda \times 45 \mathrm{h}$

$-2.08=-\lambda \times 45h$

$\lambda =0.046/\mathrm{h}$

Step 3: Expression

Now calculate the $t_{\frac{1}{2}}$ use of the following expression:

$t_{\frac{1}{2}}=\frac{0.693}{\lambda }$

$=\frac{0.693}{0.046} \mathrm{h}$

$=15.1 \mathrm{h}$

Sodium-24 has a half-life of 24 hours $15.1 \mathrm{h}$.