question_answer

Find (i) the total number of electrons, protons, neutrons and (ii) total mass of electrons, protons and neutrons present in 0.12 mg of carbon.

Answer:

Mass of carbon\[=0.12\text{ }mg\] \[=0.12\times {{10}^{-3}}g=12\times {{10}^{-5}}g\]. Total no. of electrons/protons/neutrons = no. of atoms\[\times \]total no. of electrons/protons/neutrons present in one atom of an element. No. of carbon atoms \[=\frac{Total\text{ }mass\text{ }of\text{ }carbon}{Mass\text{ }of\text{ }single\text{ }atom\text{ }of\text{ }carbon}\] Mass of single atom of carbon\[=12\text{ }amu\] \[=12\times 1.66\times {{10}^{-24}}g\]\[\left( \because 1a.m.u=1.66\times {{10}^{-24}}g \right)\] Substituting the value, we get No. of carbon atoms \[=\frac{12\times {{10}^{-5}}}{12\times 1.66\times {{10}^{-24}}}=6.023\times {{10}^{18}}\] (i) No. of electrons in 0.12 mg of carbon \[=6.023\times {{10}^{18}}\times \]no. of electrons in 1 atom of carbon \[=6.023\times {{10}^{18}}\times 6\] (ii) No. of protons in 0.12 mg of carbon \[=6.023\times {{10}^{18}}\times \]no. of protons in 1 atom of carbon \[=6.023\times {{10}^{18}}\times 6\] (iii) No. of neutrons in 0.12 mg of carbon \[=6.023\times {{10}^{18}}\times \]no. of neutrons in 1 atom of carbon \[=6.023\times {{10}^{18}}\times 6\] (iv) Total mass of electrons in 0.12 mg of carbon = Total no. of electrons in 0.12 mg of carbon\[\times \]mass of each electron. \[=6.023\times {{10}^{18}}\times 9.1\times {{10}^{28}}g\] (\[\because \]mass of one electron \[=9.1\times {{10}^{28}}g\]) (v) Total mass of protons in 0.12 mg of carbon = Total no. of protons in 0.12 mg of carbon\[\times \] mass of each proton. \[=6.023\times {{10}^{18}}\times 1.675\times {{10}^{24}}g\] (\[\because \]mass of one proton\[=1.672\times {{10}^{24}}g\]) (vi) Total mass of neutrons in 0.12 mg of carbon = Total no. of neutrons in 0.12 mg of carbon\[\times \]mass of each neutron. \[=6.023\times {{10}^{18}}\times 1.678\times {{10}^{24}}g\] (\[\because \]mass of one neutron\[=1.678\times {{10}^{24}}g\])