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# maths2 - =-=-=-= = = = = =-=-= = 7 7 7 7 2 1 2 2 2 1 2 2...

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An electron makes two jumps into different energy levels before returning to the normal state. Its behaviour is modelled approximately by the function ( 29 2 t 2 1 te t v - = where t is measured in nanoseconds (ns) and v is speed measured in femtometres per nanosecond (fmns -1 ). (a) Sketch carefully and annotate the graph of v against t for –2 ≤ t ≤ 2 and –1 ≤ v ≤1. (b) What does dt ) t ( v 2 0 represent? It represents total distance travelled by electrons in time 0 to 2 ns. (c) Evaluate this integral using the substitution u = 1 – 2t 2 - - -
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Unformatted text preview: =-=-=-= = = = = =-=-= = 7 7 7 7 2 1 2 2 2 1 2 2 4995 . ] 1 [ 2 1 | | 2 1 2 1 ) 2 ( now,-7 u 2 for t u for t du/(-2t) dt 2 2 1 , ) ( 2 2 fm e e du e t du te dt e t or tdt du t u ng substituti dt e t dt t v u u u t t (d) Hence, find the total distance travelled by the electron. fm 4995 . As calculated above (e) Sketch the graph of v(t) = ( 29 2 ) 2 t ( 2 1 e 2 t---for 0 ≤ t ≤ 4 and –1 ≤ v ≤ 1 (f) What is the total distance travelled by an electron with this speed over 4ns?...
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