Question

if the ratio of kinetic energy of Alpha particle and proton is 1:4 then ratio of this wavelength will be​

Answer 1

Given :

➾ Ratio of kinetic energy of alpha particle and proton = 1 : 4

To Find :

➛ Ratio of their wave lengths.

Solution :

➳ Relation b/w de - broglie wavelength and kinetic energy of moving particle is given by

$\bigstar\:\underline{\boxed{\tt{\lambda=\dfrac{h}{\sqrt{2m\times KE}}}}}$

where,

◕ $\lambda$ denotes wavelength

◕ h denotes plank constant

◕ m denotes mass

◕ KE denotes kinetic energy

We know that,

➝ mass of proton = m

➝ mass of alpha particle = 4m

$\longrightarrow\tt\:\dfrac{\lambda_a}{\lambda_p}=\dfrac{\sqrt{2m_p\times (KE)_p}}{\sqrt{2m_a\times (KE)_a}}\\ \\ \longrightarrow\tt\:\dfrac{\lambda_a}{\lambda_p}=\sqrt{\dfrac{m\times 4}{4m\times 1}}\\ \\ \longrightarrow\tt\:\dfrac{\lambda_a}{\lambda_p}=\sqrt{\dfrac{1}{1}}\\ \\ \longrightarrow\underline{\boxed{\bf{\lambda_a:\lambda_p=1:1}}}$