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It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called 'up' quark (denoted by u) of charge +2/3e and the down quark denoted by d) of charge (-1/3e), together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron. |
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Answer» Solution :Quark composition of PROTON : Suppose one proton is made up of `n_(1)`no. of up quark and `n_2` no. of down quark. Hence, Charge of one proton = `n_(1)`(charge of one up quark) +`n_2` (charge of one down quark) `therefore e=n_(1) ((2e)/3) + n_(2) (-e/2)`..........(1) But we are given that `n_(1) + n_(2) = 3` `therefore n_(2) =3-n_(1)`.............(2) From eqns. (1) and (2), `e = n_(1) (2e)/3 + (3-n_(1)) (-e/3)` `therefore e=(2n_(1)e)/3 - e + (n_(1)e)/3` `therefore n_(1)e = 2e` `therefore n_(1) -= 2`......(3) From eqns. (2) and (3) `n_(2) = 3-2`...........(4) `therefore n_(2) =1` Thus, one proton is made up of 2 up quarks and 1 down quark. Hence, quark composition of proton can be shown as "uud" where u = up quark and d = down quark. Quark composition of one neutron : Suppose one neutron is made up of `n_(1)`no. of up quarks and `n_2` no. of down quarks. Hence, Charge of one neutron = `n_(1)`(charge of one up quark) + `n_2` (charge of one down quark) `therefore O = n_(1) ((2e)/3) + n_(2) (-e/3)`...........(5) But we are given that `n_(1) + n_(2) =3` `therefore n_(2) = 3-n_(1)`........(6) From eqn. (5) and (6) `O = n_(1) ((2e)/3) + (3-n_(2)) (-e/3)` `therefore n_(1) =1`...........(7) From eqn. (6) and (7) `n_(2) = 3-1` `therefore n_(2) =2`...........(8) Thus, one neutron is made up of 1 up quark and 2 down quarks. Hence, quark composition of neutron can be shown as "udd". |
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