Complete the statements regarding the neutron activation of sodium and its subsequent radi… — JAMB UTME

Complete the statements regarding the neutron activation of sodium and its subsequent radioactive decay by filling in the appropriate values.

Answer:When Sodium-23 (

^{23}_{11}\text{Na}

) is bombarded with a neutron, it forms radioactive Sodium-24 (

^{24}_{11}\text{Na}

), which subsequently undergoes beta decay with a half-life of

15\text{ hours}

. Starting with an initial mass of

0.80\text{ g}

of pure

^{24}_{11}\text{Na}

, after an elapsed time of

45\text{ hours}

, the mass of

^{24}_{11}\text{Na}

remaining is 【0.1】 grams, and the element formed as the stable daughter product is 【Magnesium】.

Answer

The remaining mass of Sodium-24 after 45 hours is 0.10 grams, and the stable daughter element formed is Magnesium.

In 45 hours, exactly three 15-hour half-lives elapse, reducing the initial 0.80 g sample to 0.10 g. During beta decay, the emission of a beta particle (

^{0}_{-1}\beta

) increases the atomic number of the nuclide from 11 to 12, converting Sodium to Magnesium.

Step-by-Step Solution

Calculate the total number of half-lives elapsed (

n

)

n = \frac{t}{t_{1/2}} = \frac{45\text{ hours}}{15\text{ hours}} = 3\text{ half-lives}

The total elapsed time divided by the half-life period yields the number of decay cycles.

Determine the remaining mass of Sodium-24 using exponential decay

N_t = N_0 \times \left(\frac{1}{2}\right)^n = 0.80\text{ g} \times \left(\frac{1}{2}\right)^3 = 0.80\text{ g} \times 0.125 = 0.10\text{ g}

With each half-life cycle, the active radioactive mass decreases by half.

Write the balanced nuclear reaction for the beta decay of Sodium-24 to identify the daughter element

^{24}_{11}\text{Na} \rightarrow ^{24}_{12}\text{Mg} + ^{0}_{-1}\beta

In beta particle emission (

^{0}_{-1}\beta

), a neutron converts to a proton, increasing the atomic number

Z

from 11 to 12 while leaving the mass number

A = 24

unchanged. Element 12 on the periodic table is Magnesium (Mg).

Key Concept

Radioactive decay law and nuclear equation balancing for beta decay

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