how to calculate velocity of Alpha, Beta particles (in air, both carry 1 meV)?

Question

I couldn't find the formula for this. THe only thing i could find (both in the book and from the internet) is their ranges.

So for Alpha, its range is approximately 5.6 * 10^(-3) (m) in air

Beta's range is briefly 1 - 2 m in air

How to calculate the velocities? Isn't it equal distance/ time traveled?

I am not given the time, but given the energy. How to find out the time from the energy?

E= hc/ lambda [h and c are constants, thus lambda can be worked out, in this case lambda is wavelength]

But i'm stuck here. Please help!

Momentum "p" of the particles can be worked out (in this case they both have the same momentum since they have the same Energy), then there's this formula

p = m*v

where m = mass, v = velocity

However since ALpha & Beta have no mass, or the mass can not be used to calculate, similar to Electron, this way i'm going is wrong.

Plus i think it has something to do with their range. But i can be wrong. I'm just making guesses, trying to work this out :(

Answer 1

1MeV corresponds to the KE of the particles;
KE = 1/2mv^2

where m = the mass of the particle and v the velocity.
You will need to convert 1MeV into Joules

E= 1*10^6*1.6*10^-19 = 1.6*10^-13 Joules

So you now have v=sqrt (2*1.6*10^-19 / m)

This calculation would ignore relativistic effects. You should consider relativistic effects. Ignoring relativity will give you answers greater than the speed of light... which cannot be surpassed.

The relativistic ke equation is rather more elaborate... http://www.ux1.eiu.edu/~cfadd/1350/07WorkEnergy/RelKE.html

The mass of the alpha particle (helium nucleus) is 4*1.67*10^-27kg.
Mass of electron (beta particle) = 9.1*10^-31 kg.
You should therefore be able to calculate the velocity of each particle.

For the alpha particle, v =2.19*10^7 m/s
For the beta particle, v = 2.82*10^8 m/s

Answer 2

Beta Particle Formula

Answer 3

Use the following masses to calculate the momentum: He = 4.003 amu; electron = 1/1836 amu. The beta will be going fast enough that the relativistic formula should be used; Newtonian mechanics is adequate for the alpha. Don't worry about the air; both particles will lose energy, but that is not part of this problem.

Answer 4

Alpha particle are the Helium nuclei and mass is equal to 4 units and atomic no. is 2 and beta particles are the electrons and mass is 0 and atomic no. 1

Answer 5

You need masses for Alpha and Beta articles
Kinetic energy can be expressed as
Ke= 0.5mV^2

Then v=sqrt(2Ke/m)
Alpha partocles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus = 4 proton mass.
Beta particles are electrons so

m(Alpha)= 4 x (1.672 E−27 kg)
m(Beta)=9.109 E–31 kg

And 1 eV=1.602 E−19 Joules we have

V(alpha)=sqrt(2Ke/m)
V(alpha)=sqrt(2 x 1 E -3 eV x 1.602 E−19 J /4 x (1.672 E−27 kg)) =
V(alpha) = 210 m/s

similarly

V(beta)=sqrt(2 x 1 E-3 eV x 1.602 E−19 J / 9.109 E–31) =
= 18,760 m/s

For reference c(speed of light ) = 299,792,458m/s
so we are still safe in the inertial coordinates.