[Solved] If one of the two electrons of a H2 molecule is removed, we get a hydrogen molecular ion H2+. In the ground state of an H2+, the two protons are separated by roughly 1.5A˚ , and the electron is roughly 1A˚ from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy. - Physics Part-I

Name: Video solution 1: [Solved] If one of the two electrons of a H2 molecule is removed, we get a hydrogen molecular ion H2+. In the ground state of an H2+, the two protons are separated by roughly 1.5A˚ , and the electron is roughly 1A˚ from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy. - Physics Part-I
Uploaded: 2023-08-29T16:15:55.000Z
Duration: 17 min
Description: Video solution 1: [Solved] If one of the two electrons of a H2 molecule is removed, we get a hydrogen molecular ion H2+. In the ground state of an H2+, the two protons are separated by roughly 1.5A˚ , and the electron is roughly 1A˚ from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy. - Physics Part-I

The system of two protons and one electron is represented in the given figure.Charge on proton 1, q1=1.6×10−19CCharge on proton 2, q2=1.6×10−19CCharge on electron, q3=−1.6×10−19CDistance between protons 1 and 2, d1=1.5×10−10mDistance between proton 1 and electron, d2=1×10−10mDistance between proton 2 and electron, d3=1×10−10mThe potential energy at infinity is zero.Potential energy of the system,V=4π∈0d1q1q2+4π∈0d3q2q3+4π∈0d2q3q1Substituting 4π∈01=9×109Nm2C−2, we obtainV=10−199×109×10−19×10−19[−(16)2+1.5(1.6)2+−(1.6)2] =−30.7×10−19J =−19.2eVTherefore, the potential energy of the system is −19.2eV.

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Physics Part-I

Electrostatic Potential and Capacitance

If one of the two electrons of a H_2 molecule is removed, we g

Physics Part-I

Class 12

NCERT

Chapter 1: Electric Charges and Fields

47 questions

Chapter 2: Electrostatic Potential and Capacitance

46 questions

In a hydrogen atom, the electron and proton are bound at a distance of about

0.53 ˚ A

(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from the proton.

(b) What is the imum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?

1.06 \overset{˚}{A}

separation?

If one of the two electrons of a

H_{2}

molecule is removed, we get a hydrogen molecular ion

H_{2}^{+}

. In the ground state of an

H_{2}^{+}

, the two protons are separated by roughly

1.5 \overset{˚}{A}

, and the electron is roughly

1 \overset{˚}{A}

from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy.

Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.

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Question

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Solving time: 5 mins

If one of the two electrons of a $H_{2}$ molecule is removed, we get a hydrogen molecular ion $H_{2}^{+}$ . In the ground state of an $H_{2}^{+}$ , the two protons are separated by roughly $1.5 \overset{˚}{A}$ , and the electron is roughly $1 \overset{˚}{A}$ from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy.

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Updated on: Aug 29, 2023

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Physics Part-I (NCERT)

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If one of the two electrons of a

H_{2}

molecule is removed, we get a hydrogen molecular ion

H_{2}^{+}

. In the ground state of an

H_{2}^{+}

, the two protons are separated by roughly

1.5 \overset{˚}{A}

, and the electron is roughly

1 \overset{˚}{A}

from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy.

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

The system of two protons and one electron is represented in the given figure.

Charge on proton 1, $q_{1} = 1.6 \times 1 0^{- 19} C$

Charge on proton 2, $q_{2} = 1.6 \times 1 0^{- 19} C$

Charge on electron, $q_{3} = - 1.6 \times 1 0^{- 19} C$

Distance between protons 1 and 2, $d_{1} = 1.5 \times 1 0^{- 10} m$

Distance between proton 1 and electron, $d_{2} = 1 \times 1 0^{- 10} m$

Distance between proton 2 and electron, $d_{3} = 1 \times 1 0^{- 10} m$

The potential energy at infinity is zero.

Potential energy of the system,

$V = \frac{q _{1} q _{2}}{4 π \in _{0} d _{1}} + \frac{q _{2} q _{3}}{4 π \in _{0} d _{3}} + \frac{q _{3} q _{1}}{4 π \in _{0} d _{2}}$

Substituting $\frac{1}{4 π \in _{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2}$ , we obtain

$V = \frac{9 \times 1 0 ^{9} \times 1 0 ^{- 19} \times 1 0 ^{- 19}}{1 0 ^{- 19}} [- (16)^{2} + \frac{( 1.6 ) ^{2}}{1.5} + - (1.6)^{2}]$

$= - 30.7 \times 1 0^{- 19} J$

$= - 19.2 e V$

Therefore, the potential energy of the system is $- 19.2 e V .$

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Practice more questions from Physics Part-I (NCERT)

In a hydrogen atom, the electron and proton are bound at a distance of about

0.53 ˚ A

(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from the proton.

(b) What is the imum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?

1.06 \overset{˚}{A}

separation?

If one of the two electrons of a

H_{2}

molecule is removed, we get a hydrogen molecular ion

H_{2}^{+}

. In the ground state of an

H_{2}^{+}

, the two protons are separated by roughly

1.5 \overset{˚}{A}

, and the electron is roughly

1 \overset{˚}{A}

from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy.

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Question Text	If one of the two electrons of a $H_{2}$ molecule is removed, we get a hydrogen molecular ion $H_{2}^{+}$ . In the ground state of an $H_{2}^{+}$ , the two protons are separated by roughly $1.5 \overset{˚}{A}$ , and the electron is roughly $1 \overset{˚}{A}$ from each proton. Detere the potential energy of the system. Specify your choice of the zero of potential energy.
Updated On	Aug 29, 2023
Topic	Electrostatic Potential and Capacitance
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	222
Avg. Video Duration	17 min

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