2025 - JAMB Physics Past Questions and Answers - page 6

The wavelength of a particle is related to its momentum by the de Broglie relation, which states that
\[\lambda = \frac{h}{p}\]
where \(h\) is Planck’s constant and \(p\) is the momentum.
Since momentum is also given by \(p = mv\), the equation becomes
\[\lambda = \frac{h}{mv}\]
Rearranging to make mass the subject gives
\[m = \frac{h}{\lambda v}\]
The wavelength must first be converted to metres. Since \(1 \, \text{mm} = 10^{-3} \, \text{m}\), then
\[\lambda = 4.0 \times 10^{-7} \times 10^{-3} = 4.0 \times 10^{-10} \, \text{m}\]
Substituting the known values,
\[m = \frac{6.63 \times 10^{-34}}{(4.0 \times 10^{-10})(2.7 \times 10^{8})}\]
Multiplying the denominator gives
\[(4.0 \times 2.7) \times 10^{-10+8} = 10.8 \times 10^{-2}\]
Therefore,
\[m = \frac{6.63 \times 10^{-34}}{10.8 \times 10^{-2}}\]
This simplifies to approximately
\[m \approx 6.1 \times 10^{-31} \, \text{kg}\]
Hence, the mass of the particle is \(6.1 \times 10^{-31} \, \text{kg}\).

Refraction is the bending of light as it passes from one medium into another medium of different optical density.
In the human eye, the cornea is the transparent outer surface that first bends the incoming light rays.
The lens then further bends and focuses the light so that a clear image is formed on the retina.
Although other fluids exist in the eye, their contribution to refraction is much smaller compared to the cornea and the lens.
Therefore, the main structures responsible for refraction are the cornea and the lens.

The speed of sound in air depends mainly on the temperature and the properties of the medium.
At constant temperature, increasing the pressure also increases the density of the air in the same proportion.
Since the speed of sound depends on the ratio between pressure and density, and both change equally, their ratio remains unchanged.
As a result, the speed of sound does not change when pressure increases at constant temperature.
Therefore, the speed of sound remains unchanged.

An electrolyte is a substance that allows electric current to flow through the movement of ions.
In a wet Leclanché cell, the electrolyte used is ammonium chloride dissolved in water.
This solution provides ions that enable the chemical reactions required to produce electrical energy.
Other materials such as nickel hydroxide and lead dioxide are used in different types of batteries, but not in the wet Leclanché cell.
Therefore, the electrolyte used is ammonium chloride.

Perforated materials are capable of absorbing sound energy when sound waves strike them.
This absorption prevents sound waves from reflecting repeatedly off the walls.
When repeated reflections are reduced, the persistence of sound in the room, known as reverberation, is also reduced.
This helps improve sound clarity in the auditorium.
Therefore, lining the walls with perforated materials reduces reverberation.

Parallax occurs when the apparent position of an object changes as the observer moves relative to it.
If the object and its image move together at the same rate and in the same direction, there will be no relative shift between them.
Since there is no apparent displacement between the object and its image, parallax does not occur.
Therefore, no parallax error is observed.

In an alternating current circuit containing resistance and inductance, the impedance is found using the relation
\[Z = \sqrt{R^2 + X_L^2}\]
The inductive reactance is calculated from
\[X_L = 2\pi f L\]
Substituting the given values,
\[X_L = 2 \times \frac{22}{7} \times 50 \times 0.5\]
This becomes
\[X_L = \frac{2200}{14} = 157.14 \, \Omega\]
The impedance is then calculated as
\[Z = \sqrt{(45)^2 + (157.14)^2}\]
Squaring each term gives
\[Z = \sqrt{2025 + 24693}\]
\[Z = \sqrt{26718}\]
Taking the square root gives approximately
\[Z \approx 163.5 \, \Omega\]
Therefore, the impedance of the circuit is \(163.5 \, \Omega\).

A thermometric property is any physical property that changes in a predictable way with temperature.
Mercury expands when heated and contracts when cooled.
This change occurs in its volume, and the expansion or contraction can be measured accurately in a thermometer tube.
Because this volume change is consistent and measurable, it is used to determine temperature.
Therefore, the thermometric property of mercury is its change in volume with temperature.

The gravitational force between two objects follows the inverse square law, which states that
\[F \propto \frac{1}{r^2}\]
This means the force decreases as the square of the distance increases.
If the distance is doubled, the new distance becomes \(2r\). Substituting into the relationship gives
\[F_{new} \propto \frac{1}{(2r)^2} = \frac{1}{4r^2}\]
This shows that the new force becomes one-quarter of the original force.
Since the original force is 20 N, the new force is
\[F_{new} = \frac{20}{4} = 5 \, \text{N}\]
Therefore, the new gravitational force is 5 N.

When a conductor moves through a magnetic field or when the magnetic field around a conductor changes, a voltage is produced across the conductor. This phenomenon is explained by Faraday’s law of electromagnetic induction.
This generated voltage is called electromotive force, abbreviated as emf. It is responsible for driving electric charges through the circuit if a complete path is available.
Because this voltage is created by electromagnetic induction, it is specifically referred to as induced electromotive force.
Therefore, the correct answer is induced emf.