# How many electrons in the calcium outer shell

## Basic electrical quantities

a)given: \ (I = 10 \, \ mu \ rm {A} \ text {;} \ Delta t = 1 {,} 0 \, \ rm {a} \)

tot .: \ (\ Delta Q \)

\ [\ begin {array} {l} \ Delta Q = I \ times \ Delta t \ quad \ Rightarrow \ quad \ Delta Q = 10 \ times {10 ^ {- 6}} \ times 1.0 \ times 365 \ cdot 24 \ cdot 3600 {\ rm {As}} \ quad \ quad \ quad \ quad \ quad \ quad \ Delta Q = 315 {\ rm {As}} = 315 {\ rm {C}} \ end { array} \] A charge of approx. \ (3 {,} 2 \ cdot 10 ^ 2 \, \ rm {C} \) is driven through the circuit.

b) Charge through the line in one second: Number of electrons flowing through the cross section in one second: \ [\ begin {array} {l} \ quad \ Delta Q = I \ cdot \ Delta t \ quad \ Rightarrow \ quad \ Delta Q = 10 \ cdot {10 ^ {- 6}} \ cdot 1 {,} 0 \, {\ rm {As}} = 1 {,} 0 \ cdot {10 ^ {- 5}} {\ rm { As}} \ Delta Q = N \ cdot e \ quad \ Rightarrow \ quad N = \ frac {{\ Delta Q}} {e} \ quad \ Rightarrow \ quad N = \ frac {{1 {,} 0 \ cdot {{10} ^ {- 5}}}} {{1 {,} 6 \ cdot {{10} ^ {- 19}}}} \ frac {{{\ rm {As}}}} {{ {\ rm {As}}}} = 6 {,} 3 \ cdot {10 ^ {13}} \ end {array} \]

c) \ [\ Delta t = \ frac {N} {{4 {\ textstyle {1 \ over {\ rm {s}}}}}} \ quad \ Rightarrow \ quad \ Delta t = \ frac {{6 { ,} 3 \ cdot {{10} ^ {13}}}} {4} {\ rm {s}} = 1 {,} 6 \ cdot {10 ^ {13}} {\ rm {s}} \ quad \ Rightarrow \ quad \ Delta t = \ frac {{1 {,} 6 \ times {{10} ^ {13}}}} {{365 \ times 24 \ times 3600}} {\ rm {a}} \ approx 5 \ cdot {10 ^ 5} {\ rm {a}} \] To count the electrons flowing through the conductor cross-section in one second, one would need about 500,000 years under the given conditions.