Match List – I with List – II.
| LIST I | LIST II | ||
|---|---|---|---|
| A. | 1 GeV | I. | \( +1.6\times10^{-19}\,\mathrm{C} \) |
| B. | permittivity of free space | II. | \( 8.99\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \) |
| C. | Charge on a proton | III. | \( 8.854\times10^{-12}\,\mathrm{C^{2}\,N^{-1}\,m^{-2}} \) |
| D. | Electrostatic constant, k | IV. | \( 1.6\times10^{-10}\,\mathrm{J} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-IV, B-III, C-I, D-II
The units in List II identify each entry: joule for an energy, \( \mathrm{C^{2}\,N^{-1}\,m^{-2}} \) for a permittivity, coulomb for a charge, \( \mathrm{N\,m^{2}\,C^{-2}} \) for the constant in Coulomb’s law.
(A) 1 GeV — this matches (IV) \( 1.6\times10^{-10}\,\mathrm{J} \). The giga-electron-volt is a unit of energy, and \( 1\,\mathrm{eV} = 1.6\times10^{-19}\,\mathrm{J} \).
\( 1\,\mathrm{GeV} = 10^{9}\times1.6\times10^{-19}\,\mathrm{J} = 1.6\times10^{-10}\,\mathrm{J} \)
(B) permittivity of free space — this matches (III) \( 8.854\times10^{-12}\,\mathrm{C^{2}\,N^{-1}\,m^{-2}} \). This is the value of \( \varepsilon_0 \) in Coulomb’s law \( F = \frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^{2}} \).
(C) Charge on a proton — this matches (I) \( +1.6\times10^{-19}\,\mathrm{C} \). A proton carries the elementary charge \( +e \).
(D) Electrostatic constant, k — this matches (II) \( 8.99\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \). It is \( k = \frac{1}{4\pi\varepsilon_0} \approx 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \).
NCERT (2026-27):
Summary – “… In SI units, the unit of charge is coulomb. The experimental value of the constant ε0 is
\( \displaystyle \varepsilon_0 = 8.854 \times 10^{-12}\ \mathrm{C^2\,N^{-1}\,m^{-2}} \)
The approximate value of k is
\( \displaystyle k = 9 \times 10^{9}\ \mathrm{N\,m^2\,C^{-2}} \)”
Summary – “… Proton and electron have charges +e, –e, respectively.”
Potential Energy of a Single Charge – “… This unit of energy is defined as 1 electron volt or 1eV, i.e., 1 eV=1.6 × 10–19J. … (1 keV = 103eV = 1.6 × 10–16J, 1 MeV = 106eV = 1.6 × 10–13J, 1 GeV = 109eV = 1.6 × 10–10J and 1 TeV = 1012eV = 1.6 × 10–7J).”