Problem 14 - Master Resource Book in JEE Main Physics

Question

The mass of a particle is 400 times than that of an electron and the charge is double. The particle is accelerated by \(5 \mathrm{~V}\). Initially the particle remained in rest, then its final KE will be (a) \(10 \mathrm{eV}\) (b) \(5 \mathrm{eV}\) (c) \(50 \mathrm{eV}\) (d) \(100 \mathrm{eV}\)

Step-by-Step Solution

Answer

The final kinetic energy is 10 eV.

Step 1: Understanding the given values

The mass is given as 400 times that of an electron, and the charge is double that of an electron's charge. The electron's charge is approximately \( e = 1.6 \times 10^{-19} \) Coulombs. The particle is accelerated by a voltage of \( 5 \ \text{V} \).

Step 2: Determine particle's charge

Since the charge of the particle is double that of an electron, \( q_{\text{particle}} = 2e \).

Step 3: Calculate the kinetic energy using charge and voltage

The change in kinetic energy \( KE \) when a charge \( q \) is accelerated through a potential difference \( V \) is given by \( KE = qV \). Substituting the values, we have \( KE = (2e) \times (5 \ \text{V}) \).

Step 4: Simplify to find kinetic energy

Calculate \( KE = 2 \times e \times 5 \ \text{eV} = 10 \ \text{eV} \), since \( e \times \text{V} \) results in energy units of eV (electronvolts).

Step 5: Final Answer

Thus, the final kinetic energy of the particle when accelerated by 5V is \( 10 \ \text{eV} \).

Key Concepts

Understanding Potential Difference

Potential difference, often referred to as voltage, is a fundamental concept in physics and electronics. It represents the work needed to move a unit charge from one point to another. This is crucial because when a particle is subjected to a potential difference, it gains kinetic energy as it moves through the potential field.
To understand how potential difference operates, think of it as the "push" a charged particle needs to move. This push is provided by an external source like a battery or a power supply, which creates an electric field.

• Voltage is measured in volts (V).
• One volt means one joule of energy per coulomb of charge.

When a particle with charge moves through a potential difference, its kinetic energy changes. This is why equations like \( KE = qV \) exist. Here, energy is directly proportional both to the charge \( q \) of the particle and the voltage \( V \).
So, understanding and calculating potential difference is vital for predicting how a particle behaves under electric fields.

Charge of a Particle

In the realm of physics and chemistry, a particle's charge is one of its core properties. The charge determines how the particle interacts with other particles and fields.
The basic unit of charge is the coulomb, but in atomic and particle physics, we often use the charge of the electron as the standard. An electron has a very small charge, approximately \( e = 1.6 \times 10^{-19} \) coulombs.

• Charge affects forces between particles.
• Like charges repel, opposites attract.

In this exercise, the given particle has a charge that is twice that of an electron. Therefore, its charge \( q \) is \( 2e \). This doubled charge means that when it is subjected to a potential difference, it experiences twice the effect as a singly charged entity.
Thus, knowing the charge of a particle is key to calculating its kinetic energy change when accelerated by a potential difference.

Mass of an Electron and Particle Comparison

Mass is another fundamental property of a particle. In this exercise, knowing the mass of an electron is critical, even though the kinetic energy focus might make you think otherwise.
Electrons are very light particles with a mass about \( 9.11 \times 10^{-31} \) kg. In this problem, the mass of the particle is given as 400 times that of an electron. However, it is often the charge and potential difference that primarily determine kinetic energy.

• Mass affects inertia, not energy directly in this scenario.
• Larger mass implies greater inertia, but the energy change relies on charge and voltage.

While the mass hints at how the particle might behave if forces were applied, the main focus when assessing kinetic energy through potential difference remains on the particle's charge and the voltage applied. This underscores the importance of isolating the most relevant details from problem statements.