Which of the following particle is not deflected in the magnetic field? — Atomic Structure Chemistry Question

💡 Solution & Explanation

### Step 1 - Interaction of Moving Particles with Magnetic Fields When a moving particle enters a magnetic field, it experiences a magnetic force (\(\vec{F}_B\)) that can deflect it from its original path. This force is mathematically described by the magnetic component of the Lorentz force law: \[\vec{F}_B = q(\vec{v} \times \vec{B})\] The magnitude of this magnetic force (\(F_B\)) is given by the formula: \[F_B = |q| v B \sin\theta\] where: * \(q\) is the net electrical charge of the particle, * \(v\) is the speed of the particle, * \(B\) is the magnetic field strength, * \(\theta\) is the angle between the velocity vector (\(\vec{v}\)) of the particle and the magnetic field vector (\(\vec{B}\)). --- ### Step 2 - Condition for Zero Deflection in a Magnetic Field For a moving particle to travel through a magnetic field in a straight line without experiencing any deflection, the net magnetic force acting on it must be exactly zero: \[F_B = 0 \text{ N}\] Assuming the particle has a finite velocity (\(v \neq 0\)) and is traveling through a non-zero magnetic field (\(B \neq 0\)) at an angle not parallel or anti-parallel to the field (\(\sin\theta \neq 0\)), the magnetic force \(F_B\) can only be zero if the net electrical charge (\(q\)) of the particle is zero: \[q = 0 \text{ C}\] Therefore, only **electrically neutral particles** can pass through a magnetic field completely undeflected. --- ### Step 3 - Analyze the Electrical Charge of Each Subatomic Particle 1. **Electron:** Net Charge: \(q = -1e \approx -1.602 \times 10^{-19} \text{ C}\). Experiences magnetic force and is deflected. 2. **Proton (\ce{p^+}):** Net Charge: \(q = +1e \approx +1.602 \times 10^{-19} \text{ C}\). Experiences magnetic force and is deflected. 3. **Neutron (\ce{n^0}):** Net Charge: \(q = 0 \text{ C}\). Substituting: \(F_B = |0| \cdot vB\sin\theta = 0\). No deflection. 4. **Deuteron (\ce{d^+}):** Composed of one proton and one neutron. Net Charge: \(q = +1e\). Experiences magnetic force and is deflected. --- ### Step 4 - Systematic Analysis of the Options * **Option (A) Electron:** Incorrect. It is negatively charged and is deflected by the magnetic field. * **Option (B) Proton:** Incorrect. It is positively charged and is deflected in the direction opposite to an electron. * **Option (C) Neutron:** Correct. It is electrically neutral (\(q = 0\)) and passes through the magnetic field undeflected. * **Option (D) Deuteron:** Incorrect. It carries a net positive charge of \(+1e\) and is deflected. \[\text{Correct Option: } \boxed{\text{C}}\]