Solucions Física en context 1: Q7

Un electró té una energia en repòs de 0,511 MeV. Si l'electró es mou amb una velocitat de 0,8c, determineu:

Dades: c =3·10⁸ m·s^-1, 1eV =1,602·10^-19 J.

(a) La massa en repòs.

Primer posem l'energia en unitats del SI:

0 comma 511 space M e V times fraction numerator 10 to the power of 6 e V over denominator 1 space M e V end fraction times fraction numerator 1 comma 602 times 10 to the power of negative 19 end exponent space J over denominator 1 space e V end fraction equals 8 comma 186 times 10 to the power of negative 14 end exponent J

I la seva massa en repòs:

E subscript o equals m subscript o times c squared

8 comma 186 times 10 to the power of negative 14 end exponent equals m subscript o times left parenthesis 3 times 10 to the power of 8 right parenthesis squared

box enclose m subscript o equals 9 comma 1 times 10 to the power of negative 31 end exponent k g end enclose

(b) La massa relativista.
La massa relativista és:

m equals fraction numerator m subscript o over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction

m equals fraction numerator 9 comma 1 times 10 to the power of negative 31 end exponent over denominator square root of 1 minus begin display style fraction numerator 0 comma 8 squared times up diagonal strike c squared end strike over denominator up diagonal strike c squared end strike end fraction end style end root end fraction equals fraction numerator 9 comma 1 times 10 to the power of negative 31 end exponent over denominator square root of 1 minus 0 comma 64 end root end fraction

box enclose m equals 1 comma 52 times 10 to the power of negative 30 end exponent k g end enclose

(c) L'energia relativista total.
L'energia relativista a través de la massa relativista és:

E equals m times c squared

E equals 1 comma 52 times 10 to the power of negative 30 end exponent times left parenthesis 3 times 10 to the power of 8 right parenthesis squared

E equals 1 comma 37 times 10 to the power of negative 13 end exponent J

box enclose E equals 0 comma 854 space M e V end enclose

(d) L'energia cinètica que adquireix.
L'energia relativista total és la suma de l'energia cinètica més l'energia en repòs:

E equals E subscript c plus E subscript o

0 comma 854 equals E subscript c plus 0 comma 511

box enclose E subscript c equals 0 comma 343 space M e V end enclose