Question

The valency shell of an clement \(\Lambda\) contains 3 electrons while the valence shell of another clement \(B\) contains 6 electrons. If \(\Lambda\) combines with \(\mathrm{B}\), the probable formula of the compound formed will be (1) \(\Lambda \mathrm{B}_{2}\) (2) \(\Lambda_{2} B\) (3) \(\mathrm{A}_{2} \mathrm{~B}_{3}\) (4) \(\Lambda_{3} B_{2}\)

Short answer

Option (3): \(\Lambda_{2} \B_{3}\)

Step-by-step solution

Determine the valency of each element

Element \( \Lambda\) has 3 electrons in its valence shell, so its valency is 3, meaning it can lose 3 electrons. Element \( B\) has 6 electrons in its valence shell, giving it a valency of 2, meaning it can gain 2 electrons to complete its octet.

Find the lowest common multiple (LCM) of the valencies

The valency of \( \Lambda\) is 3 while the valency of \( B\) is 2. The lowest common multiple of 3 and 2 is 6.

Determine the ratio of atoms in which they combine

To achieve the LCM of 6, we need 2 atoms of \( \Lambda\) (since 2 x 3 = 6) and 3 atoms of \( B\) (since 3 x 2 = 6). Thus, the formula will have 2 atoms of \( \Lambda\) combine with 3 atoms of \( B\).

Write the chemical formula

Based on the ratio from Step 3, the formula of the compound formed will be \( \Lambda_{2} B_{3}\).

Verify the answer choice

From the given options, \( \Lambda_{2} \B_{3}\) corresponds to option (3).

Key concepts

chemical formula

A chemical formula represents the types and numbers of atoms in a molecule of a substance. It's like a shortcut to show how elements come together to form compounds. For example, water's chemical formula is H\textsubscript{2}O, showing that two hydrogen atoms and one oxygen atom create a water molecule.
In our exercise, we need to find how element \(\Lambda\) and element B come together to form a stable compound. By understanding their valencies and finding the most stable ratio in which they combine, we can write their chemical formula.
We know \(\Lambda\) has a valency of 3, meaning it needs to lose three electrons to reach a stable state. On the other hand, B has a valency of 2, meaning it needs to gain two electrons. This helps us form the correct chemical formula: \(\Lambda_2 B_3\).

valence electrons

Valence electrons are the outermost electrons of an atom and are crucial in determining how atoms bond with each other. They play a vital role in forming chemical bonds because they can be shared, lost, or gained to create a stable electron arrangement. The number of valence electrons varies across the periodic table.
In the given problem, element \(\Lambda\) has 3 valence electrons. This means it needs to lose these three electrons to achieve a stable electron configuration. Similarly, element B has 6 valence electrons and needs to gain 2 more electrons to complete its octet and become stable. Understanding these valence electron behaviors helps predict how these elements will combine to form a compound.
By knowing the valence electrons, we can predict the bonding patterns and final chemical formula accurately.

lowest common multiple

The lowest common multiple (LCM) helps determine the smallest number that is a multiple of two or more numbers. In chemical reactions, especially when forming compounds, the LCM helps in balancing the number of atoms required to achieve stability.
To explain using our problem, element \(\Lambda\) has a valency of 3 and element B has a valency of 2. The lowest common multiple of 3 and 2 is 6. This tells us that we need 6 electrons to balance both elements for bonding.
We can see that 2 atoms of \(\Lambda\) (2x3=6) combine with 3 atoms of B (3x2=6) to achieve a stable configuration. Hence, the simplest ratio is thus obtained, and the compound's chemical formula is \(\Lambda_2 B_3\). Understanding the LCM is essential for writing correct and balanced chemical formulas.