Question

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 :

• A. 1: √3
• B. √3 : 1
• C. 3 : 1
• D. 2 : √3

Answer 1

Answer: (B)

√3 : 1

Answer 2

$K_α = K_C$

$\frac{p^2_α}{2m_α} = \frac{p^2_c}{2m_c}$

$\frac{pα}{pc} = \sqrt{ \frac{m_α}{m_c}}$

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): $\sqrt 3 : 1$