Question

A particle of mass 3m at rest decays into two particles of masses m and 2m having non-zero velocities. The ratio of the de Broglie wavelengths of the particles ((lamda_1)/(lamda_2)) is

Answer 1

Answer:

λ1 / λ2= 1/2

Explanation:

By conservation momentum we know ,

 3mv = mv1 + 2mv2

Mass 3m is at rest so v=0

Now, 

0=mv1+2mv2 or p1+2p2=0  

here  p1 , p2 are the momentum of m and 2m resp.

Thus, ∣p1∣=2∣p2∣.............(1) 

So, 

λ1= h /∣p1∣

λ2= h /∣p2∣ 

Thus, λ1/λ2=∣p l /∣p1∣( from (1) l p1 l = 2 l p2 l

=1/2 using (1)