An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths \((λ_α :λ_{C_{12}})\) is :
- 1: √3
- √3 : 1
- 3 : 1
- 2 : √3
The Correct Option is B
Solution and Explanation
\(K_α = K_C\)
\(\frac{p^2_α}{2m_α} = \frac{p^2_c}{2m_c}\)
\(\frac{pα}{pc} = \sqrt{ \frac{m_α}{m_c}}\)
Therefore, \(\frac{λ_α}{λ_c} = \frac{h/p_α}{h/p_c} = \sqrt{\frac{m_c}{m_α}}\)
So \(\frac{λ_α}{λ_c} =\frac{ \sqrt3}{1}\)
Hence, the correct option is (B): \(\sqrt 3 : 1\)
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Concepts Used:
Kinetic Theory
The Kinetic Theory of Gases is a theory which explains the deviation of gas behaviour from ideal gases.
Postulates of Kinetic Theory of Gases:
This theory states that:
- The molecules of a gas are very small as compared to the distance between the molecules.
- A gas consists of a large number of molecules. These molecules collide with each other and the walls of the container. They obey Newton's Laws.
- There are no external forces acting on the molecules, apart from these elastic collisions.
