The Question is from neet-physics , and it was created by the author P.NARASIMHA

Question

An ionisation chamber, with parallel conducting plates as anode and cathodes has $5 	imes {10^7}{m{\;c}}{{m{m}}^{ - 3}}$ electrons and the same number of singly charged positive ions per ${m{c}}{{m{m}}^3}$. The electrons are moving toward the anode with velocity 0.4${m{m}}{{m{s}}^{ - 1}}$. The current density from anode to cathode is $4{m{\mu A}}{{m{m}}^{ - 2}}.$ The velocity of positive ions moving towards cathode is

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Current density due to moving charges
	**Related Topics**: Drift velocity, charge density, electron and ion flow
	**Prerequisites**: Understanding of current density, charge, and velocity relationship.
## SOLUTION PATHWAY
**Given Information**:
	Number density of electrons, $n_e = 5 	imes 10^7  {m{cm}}^{-3} = 5 	imes 10^{13}  {m{m}}^{-3}$
	Number density of positive ions, $n_i = 5 	imes 10^7  {m{cm}}^{-3} = 5 	imes 10^{13}  {m{m}}^{-3}$
	Velocity of electrons, $v_e = 0.4{m{m}}{{m{s}}^{ - 1}}$
	Current density, $J = 4{\mu A}{{m{m}}^{ - 2}} = 4 	imes 10^{-6} {m{A}}{{m{m}}^{ - 2}}$
	Charge of an electron, $e = 1.6 	imes 10^{-19} C$
	Important condition: Current density is from anode to cathode, which means electron flow is from cathode to anode and positive ion flow from anode to cathode.
**Method & Steps**:
	1. Calculate the current density due to electrons.
		Reasoning: Current density due to a charge is given by the product of charge density and drift velocity. Considering electrons are moving towards anode, current direction is from anode to cathode, we use absolute value for electron velocity.
		Formula/Rule: $J_e = n_e e v_e$
	2. Calculate the electron current density.
		Working: $J_e = (5 	imes 10^{13} {m{m}}^{-3}) 	imes (1.6 	imes 10^{-19} C) 	imes (0.4{m{m}}{{m{s}}^{ - 1}}) = 3.2 	imes 10^{-6} {m{A}}{{m{m}}^{ - 2}}$
		Key Point: Electron current is in the same direction as given total current density, so $J_e$ is positive.
	3. Calculate the current density due to positive ions.
		Reasoning: Total current density is sum of current densities due to electrons and positive ions.
		Formula/Rule: $J = J_e + J_i$
		Working: $J_i = J - J_e = 4 	imes 10^{-6} {m{A}}{{m{m}}^{ - 2}} - 3.2 	imes 10^{-6} {m{A}}{{m{m}}^{ - 2}} = 0.8 	imes 10^{-6} {m{A}}{{m{m}}^{ - 2}}$
	4. Calculate the velocity of positive ions.
		Reasoning: Current density due to positive ions is also given by the product of charge density and drift velocity.
		Formula/Rule: $J_i = n_i e v_i$
		Working: $v_i = \frac{J_i}{n_i e} = \frac{0.8 	imes 10^{-6} {m{A}}{{m{m}}^{ - 2}}}{(5 	imes 10^{13} {m{m}}^{-3}) 	imes (1.6 	imes 10^{-19} C)} = 0.1{m{m}}{{m{s}}^{ - 1}}$
		Result: $v_i = 0.1{m{m}}{{m{s}}^{ - 1}}$
		Verification:  The result is a reasonable drift velocity for ions and match the answer.
## OPTION ANALYSIS
[A] ✓:  The velocity of positive ions is $0.1{m{m}}{{m{s}}^{ - 1}}$.
[B] :x: This is the velocity of electrons, not the ions.
[C] :x: The ions are moving, so their velocity is not zero.
[D] :x: This is not the correct velocity of the ions.
## LEARNING AIDS
	**Common Mistakes**:
		1.  Forgetting to convert units: The number density is given in ${m{cm}}^{-3}$, it should be converted to ${m{m}}^{-3}$.
		2. Incorrect direction of current: The current direction is opposite to the direction of electron movement. 
	**Quick Tips**:
		1. Remember the formula for current density due to charge carrier $J=nev$.
		2. Pay attention to the current direction and charge type. The current due to positive charge is in the direction of its motion, and opposite to the direction of electron motion.

P.NARASIMHA · Answer

The correct Option is "$0.1\;{\rm{m}}{{\rm{s}}^{ - 1}}$"

P.NARASIMHA · Answer

$0.4\;{\rm{m}}{{\rm{s}}^{ - 1}}$

P.NARASIMHA · Answer

Zero

P.NARASIMHA · Answer

$1.6\;{\rm{m}}{{\rm{s}}^{ - 1}}$

NEET Physics MCQs

Select Chapter

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company