(a) In a quark model of elementary particles, a neutron is made of one up quarks [charge (2/3)e] and two down quarks [charges (-l/3)e]. Assume that they have a triangle configuration with side length of the order of 10^-15  Calculate electrostatic potential energy of neutron and compare it with its mass 939 MeV.

(b) Repeat above exercise for a proton which is made of two up and one down quark.

<p><span data-teams="true">This is a long answer type question as classified in NCERT Exemplar</span></p><p>Potential energy of system of charges be algebraic sum</p><p>U = <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>? </mi> <mo>? </mo> </mrow> </mrow> </mfrac> <mo> (</mo> <mfrac> <mrow> <mrow> <mi>q</mi> <mi>q</mi> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mrow> <mi>q</mi> <mi>q</mi> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mrow> <mi>q</mi> <mi>q</mi> </mrow> </mrow> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> </mfrac> <mo>)</mo> </math> </span></p><p>9<span contenteditable="false"> <math> <mo>×</mo> </math> </span>10⁹/10^-15 (1.6<span contenteditable="false"> <math> <mo>×</mo> <mn>10</mn> </math> </span>^-19)² (1/3)²- (2/3) (1/3)- (2/3) (1/3)</p><p>-7.68<span contenteditable="false"> <math> <mo>×</mo> </math> </span>10^-14J</p><p>-7.68<span contenteditable="false"> <math> <mo>×</mo> </math> </span>10^{-14<span contenteditable="false"> <math> <mo>×</mo> <mn>1.6</mn> <mo>×</mo> <mn>10</mn> </math> </span>}^-19= 0.48Mev</p>

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