The momentum (in \(\mathrm{kg}-\mathrm{m} / \mathrm{s}\) ) of photon having \(6 \mathrm{MeV}\) energy is : (a) \(3.2 \times 10^{-21}\) (b), \(2.0\) (c) \(1.6 \times 10^{-21}\) (d) none of these

Understanding the energy-momentum relation is pivotal in the realm of modern physics, particularly when dealing with particles that move at or near the speed of light. For photons, which are massless particles of light, this concept takes a special form. Unlike objects with mass, the energy (E) of a photon is directly proportional to its momentum (p), intertwined by the constant speed of light (c). This is captured in the deceivingly simple equation, \(E = pc\).

What this means is that if you know the energy of a photon, you can immediately determine its momentum, and vice versa, as long as you also know the value of the speed of light. This relationship stems from the theories of special relativity and has profound implications in fields ranging from astrophysics to quantum mechanics. To apply this fundamental principle, one must skillfully translate units and plug in the correct values, as shown in this problem where we convert energy from mega-electronvolts to joules before using the given formula.

Confronting a physics problem, one must develop a methodical approach: breaking down complex questions into manageable parts and applying physical laws step by step. Critical to this process is a thorough understanding of necessary principles, unit conversion, and manipulation of equations. In our example, the problem was unpacked in a structured manner: beginning with a unit conversion from MeV to Joules, followed by the application of the energy-momentum relation specific to photons.

While this process can seem daunting, achieving proficiency in these steps is essential for any physics student. Whether your goal is to excel in academic exams or simply to deepen your understanding of the physical world, honing your problem-solving skills is imperative. This consistent practice not only prepares you for complex problems but also builds the foundation for innovative thinking in the natural sciences.

The Joint Entrance Examination (JEE) is a highly competitive test for aspiring engineering undergraduates in India, and its preparation demands a strong grasp of concepts, particularly in physical chemistry. While our example does not directly pertain to typical physical chemistry questions, the underlying skills of unit conversion, application of scientific principles, and meticulous calculation are highly relevant.

Strong preparation for the JEE in physical chemistry involves mastering numerical problem-solving and conceptual clarity. Students should be well-versed in atomic structure, chemical kinetics, and thermodynamics, among other topics. Being familiar with the energy-momentum relation, as showcased in our example, can complement your physical chemistry studies, as it reinforces the idea that mastery of fundamental principles can be universally applied across various branches of chemistry and physics. Approaching study with this integrative mindset can greatly enhance your ability to tackle the diverse and challenging problems you will encounter on the JEE.