Advertisements
Advertisements
प्रश्न
If one of the two electrons of a H2 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 Å, and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. Specify your choice of zero potential energy.
Advertisements
उत्तर
The system of two protons and one electron is represented in the given figure.
Charge on proton 1, q1 = 1.6 × 10−19 C
Charge on proton 2, q2 = 1.6 × 10−19 C
Charge on electron, q3 = −1.6 × 10−19 C
Distance between protons 1 and 2, d1 = 1.5 × 10−10 m
Distance between proton 1 and electron, d2 = 1 × 10−10 m
Distance between proton 2 and electron, d3 = 1 × 10−10 m
The potential energy at infinity is zero.
Potential energy of the system,
`"V" = ("q"_1"q"_2)/(4piin_0"d"_1) + ("q"_2"q"_3)/(4piin_0"d"_3) + ("q"_3"q"_1)/(4piin_0"d"_2)`
Substituting `1/(4piin_0) = 9 xx 10^9 "N m"^2 "C"^-2`, we obtain
`"V" = (9 xx 10^9 xx 10^-19 xx 10^-19)/(10^-10) [-(16)^2 + (1.6)^2/(1.5) + -(1.6)^2]`
= `-30.7 xx 10^-19 "J"`
= −19.2 eV
Therefore, the potential energy of the system is −19.2 eV.
APPEARS IN
संबंधित प्रश्न
A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.
Four point charges Q, q, Q and q are placed at the corners of a square of side 'a' as shown in the figure.
Find the
1) resultant electric force on a charge Q, and
2) potential energy of this system.
Find out the amount of the work done to separate the charges at infinite distance.
A point charge Q is placed at point 'O' as shown in the figure. Is the potential at point A, i.e. VA, greater, smaller or equal to potential, VB, at point B, when Q is (i) positive, and (ii) negative charge?
1 volt is equivalent to ______.
Consider a uniform electric field in the z-direction. The potential is a constant ______.
Calculate potential energy of a point charge – q placed along the axis due to a charge +Q uniformly distributed along a ring of radius R. Sketch P.E. as a function of axial distance z from the centre of the ring. Looking at graph, can you see what would happen if – q is displaced slightly from the centre of the ring (along the axis)?
- Assertion (A): Work done in moving a charge around a closed path, in an electric field is always zero.
- Reason (R): Electrostatic force is a conservative force.
Justify your answers for each case.
State the significance of the negative value of electrostatic potential energy of a system of charges.
Three charges are placed at the corners of an equilateral triangle ABC of side 2.0 m as shown in the figure. Calculate the electric potential energy of the system of three charges.
Charges (+q) and (–q) are placed at points A and B respectively which are a distance 2L apart. C is the midpoint between A and B. What is the work done in moving a charge +Q along the semicircle CRD?
The electrostatic potential energy of a system of charges is defined as:
The electrostatic potential energy of a charge configuration is well-defined because the electrostatic force is a conservative force, which means:
For a system of unlike charges (attractive force), an external agent must do work to separate them because the system:
While assembling a system of charges, the work done in bringing the first charge \[q_1\] from infinity to its Position 1 is:
The work done in bringing charge \[q_2\] from infinity to Position 2, in the electric potential \[V_1\] produced by the fixed charge \[q_1\] at separation \[r_{12}\], is:
The total electrostatic potential energy of a two-charge system consisting of point charges \[q_1\] and \[q_2\] separated by distance \[r_{12}\] is:
For a system of n charges, the total number of unique charge pairs whose potential energies must be summed is:
For n charges \[q_1, q_2, \ldots, q_n\] at positions \[r_1, r_2, \ldots, r_n\], where \[r_{ij}\] is the distance between charge i and charge j, the total electrostatic potential energy of the system is:
For a pair of like charges, the positive potential energy (U > 0) physically signifies that:
