Answer:

To determine the number of unpaired electrons in a compound showing paramagnetism, we need to understand the concept of magnetic moment and its relation to the number of unpaired electrons.

Magnetic Moment:
The magnetic moment of a compound is a measure of its ability to be influenced by an external magnetic field. It is defined as the product of the number of unpaired electrons and the Bohr magneton (μB), which is a unit of magnetic moment.

Bohr Magneton:
The Bohr magneton (μB) is a physical constant representing the magnetic moment of an electron in the Bohr model of the atom. It is equal to 9.274 x 10^-24 Am^2.

Calculation:
Given that the magnetic moment of the compound is 54.842 x 10^-24 Am^2, we can calculate the number of unpaired electrons using the formula:

Magnetic Moment (μ) = Number of Unpaired Electrons * Bohr Magneton (μB)

54.842 x 10^-24 Am^2 = Number of Unpaired Electrons * 9.274 x 10^-24 Am^2

Dividing both sides of the equation by 9.274 x 10^-24 Am^2, we get:

Number of Unpaired Electrons = 54.842 x 10^-24 Am^2 / 9.274 x 10^-24 Am^2

Number of Unpaired Electrons = 5.92

Explanation:
According to the calculation, the number of unpaired electrons in the compound is approximately 5.92. However, since electrons cannot be fractionally present, the number must be a whole number.

In this case, we round down to the nearest whole number, which is 5. Therefore, the correct answer is 5 unpaired electrons in the compound showing paramagnetism.

Conclusion:
The compound with a magnetic moment of 54.842 x 10^-24 Am^2 (Bohr magneton) has 5 unpaired electrons. These unpaired electrons contribute to the compound's paramagnetic properties, allowing it to be influenced by an external magnetic field.