Question

Two particles A and B having Mass ratio 4:3 are Moving with kinetic energy 1:27 in ratio. What would be the ratio of wavelength sociated with particle A to that of particle 8?
a)2:3
b)9:2
c)3:4
d)06:5​

Answer 1

option B is correct answer 9:2 i hope it will help

Answer 2

Given info : Two particles A and B having mass ratio 4 : 3 are moving with kinetic enrgy 1 : 27 in ratio.

To find : the ratio of wavelength associated with particle A to that of particle B is ..

solution : According to De-Broglie's wavelength equation,

λ = h/P

where λ is wavelength associated by a particle , h is plank's constant and P is linear momentum of the particle.

we know, kinetic energy , K = P²/2m

so, P = $\sqrt{2Km}$

∴ $\lambda=\frac{h}{\sqrt{2Km}}$

here you see, wavelength is inversely proportional to $\sqrt{Km}$.

∴ $\frac{\lambda_1}{\lambda_2}=\sqrt{\frac{K_2m_2}{K_1m_1}}$

= $\sqrt{\frac{27}{1}\times\frac{3}{4}}=\sqrt{\frac{81}{4}}=\frac{9}{2}$

therefore the rato of wavelength associated with particle A to that of particle B is 9 : 2.