question_answer 20)

Calculate number of electrons which will weigh together one gram.

Answer:

Sol: Information shadow: In this problem some obvious facts have to be used, i.e., Mass of single electron \[({{m}_{e}})=9.1\times {{10}^{-28}}g\] \[=9.1\times {{10}^{-31}}kg\,\,\,...(i)\] Problem solving strategy: In this problem, it is to calculate that how many electrons will together weigh 1 g. Let x electrons will together weigh 1 g. \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,x\times {{m}_{e}}=1g\] Working it out: From eqns. (ii) and (i) \[x\times 9.1\times {{10}^{-28}}=1\] \[x=\frac{1}{9.1\times {{10}^{-28}}}1.098\times {{10}^{27}}\] (ii) Calculate the mass and charge of one mole of electrons. Sol: Information shadow: In the present problem only the name of particle is given, i.e., electron. Mass of an electron \[{{m}_{e}}=9.1\times {{10}^{-31}}kg\] Charge of an electron \[{{q}_{e}}=1.6\times {{10}^{-19}}C\] Problem solving strategy: One mole is a collection of \[6.023\times {{10}^{23}}\]particles \[\therefore \]Mass of 1 mole electrons = \[6.023\times {{10}^{23}}\times {{m}_{e}}\,\,\,\,\,\,\,\,\,\,\,....(i)\] Charge of 1 mole electrons = \[6.023\times {{10}^{23}}\times {{q}_{e}}\,\,\,\,\,\,\,\,\,\,\,....(ii)\] Working it out: From Eqn. (i): Mass of 1 mole electrons \[=6.023\times {{10}^{23}}\times 9.1\times {{10}^{-31}}\] \[=5.48\times {{10}^{-7}}kg\] From Eqn. (ii): Charge of 1 mole electrons \[=6.023\times {{10}^{23}}\times 1.6\times {{10}^{-19}}\] \[=96368C\]   DO YOU KNOW? Charge of 1 mole electron = 1 faraday 1 faraday = 96500 C (Approximately)