Question

A proton, an alpha particle and an electron are projected perpendicularly into uniform transverse electric and magnetic fields. It is observed that protons travel undeflected. Then,
(a) Deflection for alpha particle > deflection for proton
(b) Alpha particles travel in clockwise, and electron in anti-clockwise directions.
(c) Both alpha particle and electron travel without deflection
(d) Alpha particles get deflected but not electrons.

(A) Only a is correct
(B) Only b c are wrong
(C) Only d is correct
(D) a, b, d are wrong

Answer 1

Hint: It is given that a proton, an alpha particle, an electron travels perpendicular to a combined electric and magnetic field. It is said that protons travel undeflected in the combined field. We know that a charged particle is deflected by the electric and magnetic fields. Find out the reason why the proton (positively charged particle) is undeflected so that we can analyze the correct and wrong statements in the given option.

Complete step by step answer:
When deflection happens?
When a particle with a charge [charged particle] enters into the electric or magnetic field, it gets attracted or repelled by the fields. The deflection happens only when the particle has a charge.
An $\alpha - particle$ consisting of two protons and two neutrons, it is a helium nucleus. It carries two units of positive charge. $\alpha - particles$ are deflected by electric and magnetic fields as they are positively charged.
Electrons are subatomic particles with a negative charge. The electrons are deflected by the electric and magnetic field as they are negatively charged. The magnitude of electron is \[1.602176634{\text{ }} \times {\text{ }}{10^ - }^{19}C\]
Proton is a subatomic particle with a positive charge. Protons bound together with a neutron in an atom's nucleus due to the strong nuclear force. Protons are also deflected by the electric and magnetic fields. The magnitude of proton is $1.67 \times {10^{ - 27}}kg$
In the question it is given that a proton, an alpha particle and an electron are projected perpendicularly into uniform transverse electric and magnetic fields and it is observed that the proton travels undeflected. There might be only one reason for a proton to be undeflected by the transverse electric and magnetic fields. The electric field must be equal to the magnetic field. So that the electric and magnetic fields get cancelled with each other and so the proton is undeflected. If the electric and magnetic fields get cancelled then the $\alpha - particle$ and electrons also travels undeflected by the fields.
When a charged particle enters an electric field it travels in the direction of the electric field if it is a positive charge and travels in the opposite direction to the direction of the electric field if it is negative charge. When a charged particle enters a magnetic field. When a charged particle enters the magnetic field it acts perpendicular to the magnetic field. Here in the given problem both the electric and magnetic fields get cancelled so all the three particles travel in the same direction.
From the above discussion we can say that the statement given in options a) b) and d) are wrong and the option c) is correct.

Hence the correct answer is option (D) a, b, d are wrong.

Note: Protons and neutrons have the same mass [approximately]. The positive charge on a proton is equal to the negative charge on an electron in magnitude, this is the reason why an atom is neutral, when it has the same number of protons and electrons.