Speed and Momentum of a Beta Particle

[ihearyourecho]

Homework Statement

A 14C nucleus, initially at rest, emits a beta particle. The beta particle is an electron with 127 keV of kinetic energy.

A) What is the speed of the beta particle?
B) What is the momentum of the beta particle?
C) What is the momentum of the nucleus after it emits the beta particle?
D) What is the speed of the nucleus after it emits the beta particle?

Homework Equations

v = √[ 2K / m]

The Attempt at a Solution

Okay, so this is my work, but it gives the wrong answer.

Kinetic energy of beta particle K = 127 keV = 127 * 10 ^ 3 eV
= 127 * 10 ^ 3 * 1.6 * 10 ^ -19 J
= 203.2* 10^ -16 J

K = ( 1/ 2) mv ^ 2
v = √[ 2K / m]
m=9.11* 10 ^ -31 kg
v = 2.31* 10 ^ 8 m / s
THIS IS NOT RIGHT.

Can someone help me out where my thinking was flawed please?

 

[tiny-tim]

Hi ihearyourecho!

(try using the X² tag just above the Reply box )

K = ( 1/ 2) mv ^ 2
v = √[ 2K / m]
m=9.11* 10 ^ -31 kg
v = 2.31* 10 ^ 8 m / s
THIS IS NOT RIGHT.

The speed of light is c = 3*10⁸ m/s,

so your v is about 0.77 c, which is far too large to be able to use non-relativistic formulas.

You need the relativistic formula for energy. ​