Question

A neutron decays to a proton and an electron. Find the fraction of energy gone to proton if total energy released is k.m_p = 1836 m_e

• A. $\frac { 1 } { 1836 }$
• B. $\frac { 1836 } { 1837 }$
• C. $\frac { 1835 } { 1837 }$
• D. $\frac { 1 } { 1837 }$

Answer 1

Answer: (D)

$\frac { 1 } { 1837 }$

Answer 2

0 = 1836 v₁ + v₂ or v₁ = $\frac { \mathrm { v } _ { 2 } } { 1836 }$

Total KE = $\frac { 1 } { 2 }$[1836v₁² + v₂²]

=

$\frac { \mathrm { K } _ { \mathrm { P } } } { \mathrm { K } _ { \mathrm { T } } } = \frac { \frac { 1 } { 2 } \mathrm { v } _ { 2 } ^ { 2 } \times \frac { 1 } { 1836 } } { \frac { 1 } { 2 } \mathrm { v } _ { 2 } ^ { 2 } \times \frac { 1837 } { 1836 } } = \frac { 1 } { 1837 }$