An electron and a proton starting from rest get accelerated through potential difference of lOOkV. The final speeds of the electron and the proton are Ve and Vp respectively. Which of the following relations is correct?

1. Subatomic Particles: Mass and Charge Properties (basic)

To understand electricity and magnetism, we must first look at the tiny building blocks of matter: **subatomic particles**. The two most important players here are the proton and the electron. Every atom has a nucleus containing protons, which are positively charged, and electrons, which orbit the nucleus and carry a negative charge. In their natural state, atoms are neutral because the number of protons equals the number of electrons Science, class X (NCERT 2025 ed.), Metals and Non-metals, p.46. However, when an atom loses or gains electrons, it becomes an ion — a charged particle that can be influenced by electric fields Physical Geography by PMF IAS, Manjunath Thamminidi, Thunderstorm, p.348.

The defining characteristic of these particles is their charge and mass. Both the proton and the electron carry the exact same magnitude of charge, known as the elementary charge (e ≈ 1.6 × 10⁻¹⁹ Coulombs), though their signs are opposite. However, their masses are vastly different. A proton is significantly heavier — approximately 1,836 times the mass of an electron. Because electrons are so light and reside in the outer shells of an atom, they are the particles that move to create electric currents or form chemical bonds Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.59.

This difference in mass has a profound impact on how these particles behave when they move. When we apply a potential difference (Voltage), we are essentially doing work on these charges to give them Kinetic Energy (K) Science, class X (NCERT 2025 ed.), Electricity, p.174. Since the work done depends only on the charge and the voltage (K = qV), an electron and a proton accelerated through the same voltage will gain the exact same amount of energy. But because the electron is so much lighter (m is small), it must reach a much higher velocity (v) to satisfy the energy equation K = ½ mv². Think of it like a truck and a bicycle: if you give them both the same amount of "pushing energy," the bicycle will zoom away much faster than the heavy truck.

Property	Proton	Electron
Charge	Positive (+e)	Negative (-e)
Mass	Heavy (approx. 1 unit)	Negligible (approx. 1/1836 units)
Mobility	Fixed in the nucleus	Mobile; responsible for current

Sources: Science, class X (NCERT 2025 ed.), Metals and Non-metals, p.46; Physical Geography by PMF IAS, Manjunath Thamminidi, Thunderstorm, p.348; Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.59; Science, class X (NCERT 2025 ed.), Electricity, p.174

2. Electric Potential and Work Done (basic)

In our journey to understand electricity, we must first ask: what actually makes a charge move? Just as water needs a pressure difference to flow through a pipe, charges need an Electric Potential Difference (V) to move through a circuit. We define this potential difference between two points as the work done (W) to move a unit charge (Q) from one point to the other. Mathematically, this is expressed as V = W/Q. Science, Class X (NCERT 2025 ed.), Electricity, p.173

The SI unit for this "electrical pressure" is the Volt (V). One volt represents one joule of work being done to move one coulomb of charge. When a battery or power source provides this potential difference, it is essentially giving energy to the charges. If a charge Q moves through a potential V, the total work done on it—and thus the energy it gains—is W = Q × V. Science, Class X (NCERT 2025 ed.), Electricity, p.188

When a charged particle (like an electron or a proton) is accelerated from rest through a potential difference, this work done is converted entirely into Kinetic Energy (K). This leads us to a fascinating comparison between different particles:

Feature	Electron	Proton
Charge (q)	-e (1.6 × 10⁻¹⁹ C)	+e (1.6 × 10⁻¹⁹ C)
Mass (m)	Very Light	Heavy (approx. 1836 times the electron)
Kinetic Energy (qV)	Same (if V is the same)	Same (if V is the same)

Because Kinetic Energy is also defined as K = ½ mv², the mass of the particle plays a critical role in its final speed. If an electron and a proton both gain the same amount of energy (because they have the same charge magnitude), the much lighter electron must move at a significantly higher velocity to "make up" for its tiny mass in the energy equation. In contrast, the heavy proton moves much slower despite having the same energy.

Sources: Science, Class X (NCERT 2025 ed.), Electricity, p.173; Science, Class X (NCERT 2025 ed.), Electricity, p.188

3. Energy Units: The Electron Volt (eV) (intermediate)

In our everyday world, we measure energy in Joules (J), but when we zoom into the subatomic level, the Joule becomes an awkwardly large unit—like trying to measure the weight of a single grain of sand in tons. To make things manageable, physicists use the Electron Volt (eV). As we understand from the definition of potential difference, work done (W) is the product of charge (Q) and the voltage (V) it moves through, or W = Q × V Science, Class X (NCERT 2025 ed.), Electricity, p.188. One electron volt is specifically defined as the amount of kinetic energy gained by a single electron when it is accelerated from rest through a potential difference of 1 Volt.

Since the elementary charge of an electron is approximately 1.602 × 10⁻¹⁹ Coulombs, multiplying this by 1 Volt gives us the conversion factor: 1 eV = 1.602 × 10⁻¹⁹ Joules. This unit is not just for electrons; any particle with the same magnitude of charge, such as a proton, will gain exactly 1 eV of energy when moved through a 1V potential. In fact, if you have a 6V battery, it provides 6 eV of energy to every individual electron that passes through it Science, Class X (NCERT 2025 ed.), Electricity, p.174. This direct relationship makes eV the standard language for particle physics and chemistry.

A crucial distinction to master is the relationship between energy and speed. While an electron and a proton accelerated through the same voltage will gain the exact same amount of energy (measured in eV), they will not reach the same speed. This is because kinetic energy also depends on mass (K = 1/2 mv²). Because the mass of an electron is roughly 1/1836th that of a proton, the electron must travel much faster to "carry" the same amount of energy. It’s the difference between a bullet and a bowling ball—if both have the same kinetic energy, the bullet must be moving at a much higher velocity.

Feature	Electron	Proton
Charge Magnitude	e (1.6 × 10⁻¹⁹ C)	e (1.6 × 10⁻¹⁹ C)
Energy Gained in 100V	100 eV	100 eV
Relative Mass	Very Light	Heavy (~1836x electron)
Final Speed	Very High	Relatively Low

Sources: Science, Class X (NCERT 2025 ed.), Electricity, p.173; Science, Class X (NCERT 2025 ed.), Electricity, p.174; Science, Class X (NCERT 2025 ed.), Electricity, p.188

4. Applications: Particle Accelerators in India (exam-level)

In the realm of high-energy physics, a particle accelerator acts as a sophisticated engine that pushes charged particles (like electrons or protons) to incredible speeds. From a first-principles perspective, the physics begins with the concept of Work Done. When a particle with charge q is placed in an electric field and moved through a potential difference (V), the work done on it is converted entirely into Kinetic Energy (K). This is expressed by the elegant formula K = qV. If we accelerate an electron and a proton through the same potential of, say, 100 kV, both will gain exactly 100 keV of energy because they carry the same magnitude of elementary charge (e).

However, having the same energy does not mean they travel at the same speed. This is where mass comes into play. According to the classical kinetic energy formula K = ½mv², speed is inversely related to the square root of the mass for a fixed energy level. A proton is a 'heavyweight,' being approximately 1,836 times more massive than an electron. Because the electron is so much lighter, it must achieve a significantly higher velocity than the proton to possess the same amount of kinetic energy. In practical terms, while the energy gained is identical, the final speed of the electron (vₑ) is much greater than the final speed of the proton (vₚ).

India’s journey into these advanced technologies began early in its post-independence era. In August 1956, India’s first nuclear reactor, Apsara, became critical at Trombay, marking Asia's first step into the nuclear age Rajiv Ahir, A Brief History of Modern India, Developments under Nehru’s Leadership (1947-64), p.647. This paved the way for more complex installations, including Cyclotrons and Synchrotrons (like the Indus-1 and Indus-2 at the Raja Ramanna Centre for Advanced Technology in Indore). These accelerators are not just for theoretical research; they are vital for producing isotopes for cancer treatment and analyzing materials for India's growing electronics and industrial clusters Vivek Singh, Indian Economy, Infrastructure and Investment Models, p.417.

Sources: A Brief History of Modern India, Developments under Nehru’s Leadership (1947-64), p.647; Indian Economy, Infrastructure and Investment Models, p.417

5. Medical Tech: Proton Beam Therapy (intermediate)

To understand Proton Beam Therapy, we must first look at how we move these particles using Electricity and Magnetism. When a charged particle is placed in an electric field, it experiences a force. If we accelerate that particle from rest through a potential difference (V), we are doing work on it. This work is entirely converted into Kinetic Energy (K), which we calculate using the formula: K = qV. Interestingly, both a proton and an electron carry the same magnitude of elementary charge (e). This means if you accelerate a proton and an electron through the same voltage (say, 100 kV), they will both end up with the exact same amount of kinetic energy (100 keV).

However, having the same energy does not mean they behave the same way. Kinetic energy is also defined by the mass and velocity of the particle: K = ½ mv². While they share the same charge, a proton is a 'heavyweight' compared to an electron. A proton is approximately 1,836 times more massive than an electron Environment, Shankar IAS Academy, Environmental Pollution, p.82. Because the proton is so much heavier, it must move at a much lower velocity (v) to maintain the same kinetic energy as a zipping, light electron. This difference in mass and speed is why protons are so useful in medicine; their momentum allows them to travel in a straight path through tissue, much like how a laser beam follows a straight path in water Science-Class VII, NCERT, Light: Shadows and Reflections, p.156, but with the added ability to stop exactly where we want them to.

In cancer treatment, this precision is vital. Unlike ionizing radiations like X-rays or UV rays which can cause broad damage to DNA and tissues Environment, Shankar IAS Academy, Ozone Depletion, p.271, the 'heavy' nature of protons allows doctors to target a tumor with surgical accuracy. By controlling the speed of these heavy particles, we ensure they release their destructive energy only when they reach the cancer cells, minimizing the short-range and long-range side effects like burns or impaired metabolism usually associated with radiation Environment, Shankar IAS Academy, Environmental Pollution, p.83. This builds on the legacy of researchers like Dr. Kamal Ranadive, who dedicated their lives to improving cancer treatment and prevention Science, Class VIII, NCERT, Health: The Ultimate Treasure, p.37.

Feature	Electron	Proton
Charge Magnitude	1e (Negative)	1e (Positive)
Mass	Very Light (~1/1836 amu)	Heavy (~1 amu)
Velocity (at same K)	Much Higher	Much Lower
Usage in Therapy	Surface/Shallow treatment	Deep, Precise targeting

Sources: Environment, Shankar IAS Academy, Environmental Pollution, p.82; Science-Class VII, NCERT, Light: Shadows and Reflections, p.156; Environment, Shankar IAS Academy, Ozone Depletion, p.271; Environment, Shankar IAS Academy, Environmental Pollution, p.83; Science, Class VIII, NCERT, Health: The Ultimate Treasure, p.37

6. Physics of Motion: Kinetic Energy and Velocity (intermediate)

To understand how charged particles behave in an electric field, we must bridge the gap between electrical potential and mechanical motion. When a charged particle is accelerated from rest through a potential difference ($V$), the work done on that particle by the electric field is converted into Kinetic Energy ($K$), which is the energy of motion (Environment and Ecology, Majid Hussain, Major Crops and Cropping Patterns in India, p.113). This relationship is expressed as $K = qV$. If we take an electron and a proton, both carry the same magnitude of elementary charge ($e$), meaning if they are accelerated through the same voltage, they will gain the exact same amount of kinetic energy.

However, equal energy does not translate to equal speed. The formula for kinetic energy is $K = 1/2 mv²$, where $m$ represents mass and $v$ represents velocity (Science-Class VII, NCERT, Measurement of Time and Motion, p.119). Because the mass of an electron is approximately 1/1836 times the mass of a proton, the electron is much "lighter." To satisfy the equation where $K$ remains constant, the electron must achieve a much higher velocity than the proton. This is a crucial concept in particle physics: for a given energy level, velocity is inversely proportional to the square root of the mass ($v ∝ 1/√m$).

Feature	Electron	Proton
Charge Magnitude	$e$ (same)	$e$ (same)
Mass	Very Small	Relatively Large
Kinetic Energy (at same $V$)	Identical	Identical
Final Velocity	Significantly Higher	Lower

Sources: Environment and Ecology, Majid Hussain, Major Crops and Cropping Patterns in India, p.113; Science-Class VII, NCERT, Measurement of Time and Motion, p.119

7. Solving the Original PYQ (exam-level)

Review the concepts above and try solving the question.